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<h1 class="epydoc">Source Code for <a href="numdifftools.core-module.html">Module numdifftools.core</a></h1>
<pre class="py-src">
<a name="L1"></a><tt class="py-lineno">   1</tt>  <tt class="py-line"><tt class="py-docstring">"""</tt> </tt>
<a name="L2"></a><tt class="py-lineno">   2</tt>  <tt class="py-line"><tt class="py-docstring">Numdifftools implementation</tt> </tt>
<a name="L3"></a><tt class="py-lineno">   3</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L4"></a><tt class="py-lineno">   4</tt>  <tt class="py-line"><tt class="py-docstring">"""</tt> </tt>
<a name="L5"></a><tt class="py-lineno">   5</tt>  <tt class="py-line"><tt class="py-comment">#-------------------------------------------------------------------------</tt> </tt>
<a name="L6"></a><tt class="py-lineno">   6</tt>  <tt class="py-line"><tt class="py-comment">#Author:      Per A. Brodtkorb</tt> </tt>
<a name="L7"></a><tt class="py-lineno">   7</tt>  <tt class="py-line"><tt class="py-comment">#</tt> </tt>
<a name="L8"></a><tt class="py-lineno">   8</tt>  <tt class="py-line"><tt class="py-comment"># Created:     01.08.2008</tt> </tt>
<a name="L9"></a><tt class="py-lineno">   9</tt>  <tt class="py-line"><tt class="py-comment"># Copyright:   (c) pab 2008</tt> </tt>
<a name="L10"></a><tt class="py-lineno">  10</tt>  <tt class="py-line"><tt class="py-comment"># Licence:     New BSD</tt> </tt>
<a name="L11"></a><tt class="py-lineno">  11</tt>  <tt class="py-line"><tt class="py-comment">#</tt> </tt>
<a name="L12"></a><tt class="py-lineno">  12</tt>  <tt class="py-line"><tt class="py-comment"># Based on matlab functions derivest.m gradest.m hessdiag.m, hessian.m</tt> </tt>
<a name="L13"></a><tt class="py-lineno">  13</tt>  <tt class="py-line"><tt class="py-comment"># and jacobianest.m by:</tt> </tt>
<a name="L14"></a><tt class="py-lineno">  14</tt>  <tt class="py-line"><tt class="py-comment">#</tt> </tt>
<a name="L15"></a><tt class="py-lineno">  15</tt>  <tt class="py-line"><tt class="py-comment"># Author: John D'Errico</tt> </tt>
<a name="L16"></a><tt class="py-lineno">  16</tt>  <tt class="py-line"><tt class="py-comment"># e-mail: woodchips@rochester.rr.com</tt> </tt>
<a name="L17"></a><tt class="py-lineno">  17</tt>  <tt class="py-line"><tt class="py-comment"># Release: 1.0</tt> </tt>
<a name="L18"></a><tt class="py-lineno">  18</tt>  <tt class="py-line"><tt class="py-comment"># Release date: 12/27/2006</tt> </tt>
<a name="L19"></a><tt class="py-lineno">  19</tt>  <tt class="py-line"><tt class="py-comment">#-------------------------------------------------------------------------</tt> </tt>
<a name="L20"></a><tt class="py-lineno">  20</tt>  <tt class="py-line"><tt class="py-comment">#!/usr/bin/env python</tt> </tt>
<a name="L21"></a><tt class="py-lineno">  21</tt>  <tt class="py-line"> </tt>
<a name="L22"></a><tt class="py-lineno">  22</tt>  <tt class="py-line"><tt class="py-keyword">from</tt> <tt class="py-name">__future__</tt> <tt class="py-keyword">import</tt> <tt class="py-name">division</tt> </tt>
<a name="L23"></a><tt class="py-lineno">  23</tt>  <tt class="py-line"><tt class="py-keyword">import</tt> <tt class="py-name">numpy</tt> <tt class="py-keyword">as</tt> <tt class="py-name">np</tt> </tt>
<a name="L24"></a><tt class="py-lineno">  24</tt>  <tt class="py-line"><tt class="py-keyword">import</tt> <tt class="py-name">scipy</tt><tt class="py-op">.</tt><tt class="py-name">linalg</tt> <tt class="py-keyword">as</tt> <tt class="py-name">linalg</tt> </tt>
<a name="L25"></a><tt class="py-lineno">  25</tt>  <tt class="py-line"><tt class="py-comment">#import numpy.linalg as linalg</tt> </tt>
<a name="L26"></a><tt class="py-lineno">  26</tt>  <tt class="py-line"><tt class="py-keyword">import</tt> <tt class="py-name">scipy</tt><tt class="py-op">.</tt><tt class="py-name">misc</tt> <tt class="py-keyword">as</tt> <tt class="py-name">misc</tt> </tt>
<a name="L27"></a><tt class="py-lineno">  27</tt>  <tt class="py-line"><tt class="py-keyword">import</tt> <tt class="py-name">warnings</tt> </tt>
<a name="L28"></a><tt class="py-lineno">  28</tt>  <tt class="py-line"> </tt>
<a name="L29"></a><tt class="py-lineno">  29</tt>  <tt class="py-line"><tt class="py-name">__all__</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt> </tt>
<a name="L30"></a><tt class="py-lineno">  30</tt>  <tt class="py-line">    <tt class="py-string">'dea3'</tt><tt class="py-op">,</tt> <tt class="py-string">'Derivative'</tt><tt class="py-op">,</tt> <tt class="py-string">'Jacobian'</tt><tt class="py-op">,</tt> <tt class="py-string">'Gradient'</tt><tt class="py-op">,</tt> <tt class="py-string">'Hessian'</tt><tt class="py-op">,</tt> <tt class="py-string">'Hessdiag'</tt> </tt>
<a name="L31"></a><tt class="py-lineno">  31</tt>  <tt class="py-line">    <tt class="py-op">]</tt> </tt>
<a name="L32"></a><tt class="py-lineno">  32</tt>  <tt class="py-line"> </tt>
<a name="L33"></a><tt class="py-lineno">  33</tt>  <tt class="py-line"><tt id="link-0" class="py-name" targets="Variable numdifftools.core._TINY=numdifftools.core-module.html#_TINY"><a title="numdifftools.core._TINY" class="py-name" href="#" onclick="return doclink('link-0', '_TINY', 'link-0');">_TINY</a></tt> <tt class="py-op">=</tt>  <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">finfo</tt><tt class="py-op">(</tt><tt class="py-name">float</tt><tt class="py-op">)</tt><tt class="py-op">.</tt><tt class="py-name">machar</tt><tt class="py-op">.</tt><tt class="py-name">tiny</tt> </tt>
<a name="L34"></a><tt class="py-lineno">  34</tt>  <tt class="py-line"><tt id="link-1" class="py-name" targets="Variable numdifftools.core._EPS=numdifftools.core-module.html#_EPS"><a title="numdifftools.core._EPS" class="py-name" href="#" onclick="return doclink('link-1', '_EPS', 'link-1');">_EPS</a></tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">finfo</tt><tt class="py-op">(</tt><tt class="py-name">float</tt><tt class="py-op">)</tt><tt class="py-op">.</tt><tt class="py-name">machar</tt><tt class="py-op">.</tt><tt class="py-name">eps</tt> </tt>
<a name="dea3"></a><div id="dea3-def"><a name="L35"></a><tt class="py-lineno">  35</tt> <a class="py-toggle" href="#" id="dea3-toggle" onclick="return toggle('dea3');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core-module.html#dea3">dea3</a><tt class="py-op">(</tt><tt class="py-param">v0</tt><tt class="py-op">,</tt> <tt class="py-param">v1</tt><tt class="py-op">,</tt> <tt class="py-param">v2</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="dea3-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="dea3-expanded"><a name="L36"></a><tt class="py-lineno">  36</tt>  <tt class="py-line">    <tt class="py-docstring">'''</tt> </tt>
<a name="L37"></a><tt class="py-lineno">  37</tt>  <tt class="py-line"><tt class="py-docstring">    Extrapolate a slowly convergent sequence</tt> </tt>
<a name="L38"></a><tt class="py-lineno">  38</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L39"></a><tt class="py-lineno">  39</tt>  <tt class="py-line"><tt class="py-docstring">    Parameters</tt> </tt>
<a name="L40"></a><tt class="py-lineno">  40</tt>  <tt class="py-line"><tt class="py-docstring">    ----------</tt> </tt>
<a name="L41"></a><tt class="py-lineno">  41</tt>  <tt class="py-line"><tt class="py-docstring">    v0, v1, v2 : array-like</tt> </tt>
<a name="L42"></a><tt class="py-lineno">  42</tt>  <tt class="py-line"><tt class="py-docstring">        3 values of a convergent sequence to extrapolate</tt> </tt>
<a name="L43"></a><tt class="py-lineno">  43</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L44"></a><tt class="py-lineno">  44</tt>  <tt class="py-line"><tt class="py-docstring">    Returns</tt> </tt>
<a name="L45"></a><tt class="py-lineno">  45</tt>  <tt class="py-line"><tt class="py-docstring">    -------</tt> </tt>
<a name="L46"></a><tt class="py-lineno">  46</tt>  <tt class="py-line"><tt class="py-docstring">    result : array-like</tt> </tt>
<a name="L47"></a><tt class="py-lineno">  47</tt>  <tt class="py-line"><tt class="py-docstring">        extrapolated value</tt> </tt>
<a name="L48"></a><tt class="py-lineno">  48</tt>  <tt class="py-line"><tt class="py-docstring">    abserr : array-like</tt> </tt>
<a name="L49"></a><tt class="py-lineno">  49</tt>  <tt class="py-line"><tt class="py-docstring">        absolute error estimate</tt> </tt>
<a name="L50"></a><tt class="py-lineno">  50</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L51"></a><tt class="py-lineno">  51</tt>  <tt class="py-line"><tt class="py-docstring">    Description</tt> </tt>
<a name="L52"></a><tt class="py-lineno">  52</tt>  <tt class="py-line"><tt class="py-docstring">    -----------</tt> </tt>
<a name="L53"></a><tt class="py-lineno">  53</tt>  <tt class="py-line"><tt class="py-docstring">    DEA3 attempts to extrapolate nonlinearly to a better estimate</tt> </tt>
<a name="L54"></a><tt class="py-lineno">  54</tt>  <tt class="py-line"><tt class="py-docstring">    of the sequence's limiting value, thus improving the rate of</tt> </tt>
<a name="L55"></a><tt class="py-lineno">  55</tt>  <tt class="py-line"><tt class="py-docstring">    convergence. The routine is based on the epsilon algorithm of</tt> </tt>
<a name="L56"></a><tt class="py-lineno">  56</tt>  <tt class="py-line"><tt class="py-docstring">    P. Wynn, see [1]_.</tt> </tt>
<a name="L57"></a><tt class="py-lineno">  57</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L58"></a><tt class="py-lineno">  58</tt>  <tt class="py-line"><tt class="py-docstring">     Example</tt> </tt>
<a name="L59"></a><tt class="py-lineno">  59</tt>  <tt class="py-line"><tt class="py-docstring">     -------</tt> </tt>
<a name="L60"></a><tt class="py-lineno">  60</tt>  <tt class="py-line"><tt class="py-docstring">     # integrate sin(x) from 0 to pi/2</tt> </tt>
<a name="L61"></a><tt class="py-lineno">  61</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L62"></a><tt class="py-lineno">  62</tt>  <tt class="py-line"><tt class="py-docstring">     &gt;&gt;&gt; import numpy as np</tt> </tt>
<a name="L63"></a><tt class="py-lineno">  63</tt>  <tt class="py-line"><tt class="py-docstring">     &gt;&gt;&gt; import numdifftools as nd</tt> </tt>
<a name="L64"></a><tt class="py-lineno">  64</tt>  <tt class="py-line"><tt class="py-docstring">     &gt;&gt;&gt; Ei= np.zeros(3)</tt> </tt>
<a name="L65"></a><tt class="py-lineno">  65</tt>  <tt class="py-line"><tt class="py-docstring">     &gt;&gt;&gt; linfun = lambda k : np.linspace(0,np.pi/2.,2.**(k+5)+1)</tt> </tt>
<a name="L66"></a><tt class="py-lineno">  66</tt>  <tt class="py-line"><tt class="py-docstring">     &gt;&gt;&gt; for k in np.arange(3): </tt> </tt>
<a name="L67"></a><tt class="py-lineno">  67</tt>  <tt class="py-line"><tt class="py-docstring">     ...    x = linfun(k) </tt> </tt>
<a name="L68"></a><tt class="py-lineno">  68</tt>  <tt class="py-line"><tt class="py-docstring">     ...    Ei[k] = np.trapz(np.sin(x),x)</tt> </tt>
<a name="L69"></a><tt class="py-lineno">  69</tt>  <tt class="py-line"><tt class="py-docstring">     &gt;&gt;&gt; [En, err] = nd.dea3(Ei[0], Ei[1], Ei[2])</tt> </tt>
<a name="L70"></a><tt class="py-lineno">  70</tt>  <tt class="py-line"><tt class="py-docstring">     &gt;&gt;&gt; truErr = Ei-1.</tt> </tt>
<a name="L71"></a><tt class="py-lineno">  71</tt>  <tt class="py-line"><tt class="py-docstring">     &gt;&gt;&gt; (truErr, err, En)</tt> </tt>
<a name="L72"></a><tt class="py-lineno">  72</tt>  <tt class="py-line"><tt class="py-docstring">     (array([ -2.00805680e-04,  -5.01999079e-05,  -1.25498825e-05]), array([ 0.00020081]), array([ 1.]))</tt> </tt>
<a name="L73"></a><tt class="py-lineno">  73</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L74"></a><tt class="py-lineno">  74</tt>  <tt class="py-line"><tt class="py-docstring">     See also</tt> </tt>
<a name="L75"></a><tt class="py-lineno">  75</tt>  <tt class="py-line"><tt class="py-docstring">     --------</tt> </tt>
<a name="L76"></a><tt class="py-lineno">  76</tt>  <tt class="py-line"><tt class="py-docstring">     dea</tt> </tt>
<a name="L77"></a><tt class="py-lineno">  77</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L78"></a><tt class="py-lineno">  78</tt>  <tt class="py-line"><tt class="py-docstring">     Reference</tt> </tt>
<a name="L79"></a><tt class="py-lineno">  79</tt>  <tt class="py-line"><tt class="py-docstring">     ---------</tt> </tt>
<a name="L80"></a><tt class="py-lineno">  80</tt>  <tt class="py-line"><tt class="py-docstring">     .. [1] C. Brezinski (1977)</tt> </tt>
<a name="L81"></a><tt class="py-lineno">  81</tt>  <tt class="py-line"><tt class="py-docstring">            "Acceleration de la convergence en analyse numerique",</tt> </tt>
<a name="L82"></a><tt class="py-lineno">  82</tt>  <tt class="py-line"><tt class="py-docstring">            "Lecture Notes in Math.", vol. 584,</tt> </tt>
<a name="L83"></a><tt class="py-lineno">  83</tt>  <tt class="py-line"><tt class="py-docstring">            Springer-Verlag, New York, 1977.</tt> </tt>
<a name="L84"></a><tt class="py-lineno">  84</tt>  <tt class="py-line"><tt class="py-docstring">    '''</tt> </tt>
<a name="L85"></a><tt class="py-lineno">  85</tt>  <tt class="py-line"> </tt>
<a name="L86"></a><tt class="py-lineno">  86</tt>  <tt class="py-line">    <tt class="py-name">E0</tt><tt class="py-op">,</tt> <tt class="py-name">E1</tt><tt class="py-op">,</tt> <tt class="py-name">E2</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">atleast_1d</tt><tt class="py-op">(</tt><tt class="py-name">v0</tt><tt class="py-op">,</tt> <tt class="py-name">v1</tt><tt class="py-op">,</tt> <tt class="py-name">v2</tt><tt class="py-op">)</tt> </tt>
<a name="L87"></a><tt class="py-lineno">  87</tt>  <tt class="py-line">    <tt class="py-name">abs</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">abs</tt> <tt class="py-comment">#@ReservedAssignment</tt> </tt>
<a name="L88"></a><tt class="py-lineno">  88</tt>  <tt class="py-line">    <tt class="py-name">max</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">maximum</tt> <tt class="py-comment">#@ReservedAssignment</tt> </tt>
<a name="L89"></a><tt class="py-lineno">  89</tt>  <tt class="py-line">    <tt class="py-name">zeros</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt> </tt>
<a name="L90"></a><tt class="py-lineno">  90</tt>  <tt class="py-line">    <tt class="py-name">ten</tt> <tt class="py-op">=</tt> <tt class="py-number">10.0</tt> </tt>
<a name="L91"></a><tt class="py-lineno">  91</tt>  <tt class="py-line">    <tt class="py-name">one</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">ones</tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">)</tt> </tt>
<a name="L92"></a><tt class="py-lineno">  92</tt>  <tt class="py-line">    <tt class="py-name">small</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">finfo</tt><tt class="py-op">(</tt><tt class="py-name">float</tt><tt class="py-op">)</tt><tt class="py-op">.</tt><tt class="py-name">eps</tt>  <tt class="py-comment">#1.0e-16 #spacing(one)</tt> </tt>
<a name="L93"></a><tt class="py-lineno">  93</tt>  <tt class="py-line">    <tt class="py-name">delta2</tt> <tt class="py-op">=</tt> <tt class="py-name">E2</tt> <tt class="py-op">-</tt> <tt class="py-name">E1</tt> </tt>
<a name="L94"></a><tt class="py-lineno">  94</tt>  <tt class="py-line">    <tt class="py-name">delta1</tt> <tt class="py-op">=</tt> <tt class="py-name">E1</tt> <tt class="py-op">-</tt> <tt class="py-name">E0</tt> </tt>
<a name="L95"></a><tt class="py-lineno">  95</tt>  <tt class="py-line">    <tt class="py-name">err2</tt> <tt class="py-op">=</tt> <tt class="py-name">abs</tt><tt class="py-op">(</tt><tt class="py-name">delta2</tt><tt class="py-op">)</tt> </tt>
<a name="L96"></a><tt class="py-lineno">  96</tt>  <tt class="py-line">    <tt class="py-name">err1</tt> <tt class="py-op">=</tt> <tt class="py-name">abs</tt><tt class="py-op">(</tt><tt class="py-name">delta1</tt><tt class="py-op">)</tt> </tt>
<a name="L97"></a><tt class="py-lineno">  97</tt>  <tt class="py-line">    <tt class="py-name">tol2</tt> <tt class="py-op">=</tt> <tt class="py-name">max</tt><tt class="py-op">(</tt><tt class="py-name">abs</tt><tt class="py-op">(</tt><tt class="py-name">E2</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">abs</tt><tt class="py-op">(</tt><tt class="py-name">E1</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">small</tt> </tt>
<a name="L98"></a><tt class="py-lineno">  98</tt>  <tt class="py-line">    <tt class="py-name">tol1</tt> <tt class="py-op">=</tt> <tt class="py-name">max</tt><tt class="py-op">(</tt><tt class="py-name">abs</tt><tt class="py-op">(</tt><tt class="py-name">E1</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">abs</tt><tt class="py-op">(</tt><tt class="py-name">E0</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">small</tt> </tt>
<a name="L99"></a><tt class="py-lineno">  99</tt>  <tt class="py-line"> </tt>
<a name="L100"></a><tt class="py-lineno"> 100</tt>  <tt class="py-line">    <tt class="py-name">result</tt> <tt class="py-op">=</tt> <tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-name">E0</tt><tt class="py-op">.</tt><tt class="py-name">shape</tt><tt class="py-op">)</tt> </tt>
<a name="L101"></a><tt class="py-lineno"> 101</tt>  <tt class="py-line">    <tt class="py-name">abserr</tt> <tt class="py-op">=</tt> <tt class="py-name">result</tt><tt class="py-op">.</tt><tt class="py-name">copy</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L102"></a><tt class="py-lineno"> 102</tt>  <tt class="py-line">    <tt class="py-name">converged</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">err1</tt> <tt class="py-op">&lt;=</tt> <tt class="py-name">tol1</tt><tt class="py-op">)</tt> <tt class="py-op">&amp;</tt> <tt class="py-op">(</tt><tt class="py-name">err2</tt> <tt class="py-op">&lt;=</tt> <tt class="py-name">tol2</tt><tt class="py-op">)</tt><tt class="py-op">.</tt><tt class="py-name">ravel</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L103"></a><tt class="py-lineno"> 103</tt>  <tt class="py-line">    <tt class="py-name">k0</tt><tt class="py-op">,</tt> <tt class="py-op">=</tt> <tt class="py-name">converged</tt><tt class="py-op">.</tt><tt class="py-name">nonzero</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L104"></a><tt class="py-lineno"> 104</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">k0</tt><tt class="py-op">.</tt><tt class="py-name">size</tt> <tt class="py-op">&gt;</tt> <tt class="py-number">0</tt> <tt class="py-op">:</tt> </tt>
<a name="L105"></a><tt class="py-lineno"> 105</tt>  <tt class="py-line">        <tt class="py-comment"># IF E0, E1 AND E2 ARE EQUAL TO WITHIN MACHINE</tt> </tt>
<a name="L106"></a><tt class="py-lineno"> 106</tt>  <tt class="py-line">        <tt class="py-comment">#   ACCURACY, CONVERGENCE IS ASSUMED.</tt> </tt>
<a name="L107"></a><tt class="py-lineno"> 107</tt>  <tt class="py-line">        <tt class="py-name">result</tt><tt class="py-op">[</tt><tt class="py-name">k0</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">E2</tt><tt class="py-op">[</tt><tt class="py-name">k0</tt><tt class="py-op">]</tt> </tt>
<a name="L108"></a><tt class="py-lineno"> 108</tt>  <tt class="py-line">        <tt class="py-name">abserr</tt><tt class="py-op">[</tt><tt class="py-name">k0</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">err1</tt><tt class="py-op">[</tt><tt class="py-name">k0</tt><tt class="py-op">]</tt> <tt class="py-op">+</tt> <tt class="py-name">err2</tt><tt class="py-op">[</tt><tt class="py-name">k0</tt><tt class="py-op">]</tt> <tt class="py-op">+</tt> <tt class="py-name">E2</tt><tt class="py-op">[</tt><tt class="py-name">k0</tt><tt class="py-op">]</tt> <tt class="py-op">*</tt> <tt class="py-name">small</tt> <tt class="py-op">*</tt> <tt class="py-name">ten</tt> </tt>
<a name="L109"></a><tt class="py-lineno"> 109</tt>  <tt class="py-line"> </tt>
<a name="L110"></a><tt class="py-lineno"> 110</tt>  <tt class="py-line">    <tt class="py-name">k1</tt><tt class="py-op">,</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-number">1</tt> <tt class="py-op">-</tt> <tt class="py-name">converged</tt><tt class="py-op">)</tt><tt class="py-op">.</tt><tt class="py-name">nonzero</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L111"></a><tt class="py-lineno"> 111</tt>  <tt class="py-line"> </tt>
<a name="L112"></a><tt class="py-lineno"> 112</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">k1</tt><tt class="py-op">.</tt><tt class="py-name">size</tt> <tt class="py-op">&gt;</tt> <tt class="py-number">0</tt> <tt class="py-op">:</tt> </tt>
<a name="L113"></a><tt class="py-lineno"> 113</tt>  <tt class="py-line">        <tt class="py-keyword">with</tt> <tt class="py-name">warnings</tt><tt class="py-op">.</tt><tt class="py-name">catch_warnings</tt><tt class="py-op">(</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L114"></a><tt class="py-lineno"> 114</tt>  <tt class="py-line">            <tt class="py-name">warnings</tt><tt class="py-op">.</tt><tt class="py-name">simplefilter</tt><tt class="py-op">(</tt><tt class="py-string">"ignore"</tt><tt class="py-op">)</tt> <tt class="py-comment"># ignore division by zero and overflow</tt> </tt>
<a name="L115"></a><tt class="py-lineno"> 115</tt>  <tt class="py-line"><tt class="py-comment">#            t1 = np.where(delta1[k1]==0, _TINY,0) # avoid division by zero </tt> </tt>
<a name="L116"></a><tt class="py-lineno"> 116</tt>  <tt class="py-line"><tt class="py-comment">#            t2 = np.where(delta2[k1]==0, _TINY,0)</tt> </tt>
<a name="L117"></a><tt class="py-lineno"> 117</tt>  <tt class="py-line"><tt class="py-comment">#            ss = one / (delta2[k1] + t2) - one / (delta1[k1] + t1)</tt> </tt>
<a name="L118"></a><tt class="py-lineno"> 118</tt>  <tt class="py-line">            <tt class="py-name">ss</tt> <tt class="py-op">=</tt> <tt class="py-name">one</tt> <tt class="py-op">/</tt> <tt class="py-name">delta2</tt><tt class="py-op">[</tt><tt class="py-name">k1</tt><tt class="py-op">]</tt> <tt class="py-op">-</tt> <tt class="py-name">one</tt> <tt class="py-op">/</tt> <tt class="py-name">delta1</tt><tt class="py-op">[</tt><tt class="py-name">k1</tt><tt class="py-op">]</tt> </tt>
<a name="L119"></a><tt class="py-lineno"> 119</tt>  <tt class="py-line">            <tt class="py-name">smallE2</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">abs</tt><tt class="py-op">(</tt><tt class="py-name">ss</tt> <tt class="py-op">*</tt> <tt class="py-name">E1</tt><tt class="py-op">[</tt><tt class="py-name">k1</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> <tt class="py-op">&lt;=</tt> <tt class="py-number">1.0e-3</tt><tt class="py-op">)</tt><tt class="py-op">.</tt><tt class="py-name">ravel</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L120"></a><tt class="py-lineno"> 120</tt>  <tt class="py-line">        <tt class="py-name">k2</tt> <tt class="py-op">=</tt> <tt class="py-name">k1</tt><tt class="py-op">[</tt><tt class="py-name">smallE2</tt><tt class="py-op">.</tt><tt class="py-name">nonzero</tt><tt class="py-op">(</tt><tt class="py-op">)</tt><tt class="py-op">]</tt> </tt>
<a name="L121"></a><tt class="py-lineno"> 121</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">k2</tt><tt class="py-op">.</tt><tt class="py-name">size</tt> <tt class="py-op">&gt;</tt> <tt class="py-number">0</tt> <tt class="py-op">:</tt> </tt>
<a name="L122"></a><tt class="py-lineno"> 122</tt>  <tt class="py-line">            <tt class="py-name">result</tt><tt class="py-op">[</tt><tt class="py-name">k2</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">E2</tt><tt class="py-op">[</tt><tt class="py-name">k2</tt><tt class="py-op">]</tt> </tt>
<a name="L123"></a><tt class="py-lineno"> 123</tt>  <tt class="py-line">            <tt class="py-name">abserr</tt><tt class="py-op">[</tt><tt class="py-name">k2</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">err1</tt><tt class="py-op">[</tt><tt class="py-name">k2</tt><tt class="py-op">]</tt> <tt class="py-op">+</tt> <tt class="py-name">err2</tt><tt class="py-op">[</tt><tt class="py-name">k2</tt><tt class="py-op">]</tt> <tt class="py-op">+</tt> <tt class="py-name">E2</tt><tt class="py-op">[</tt><tt class="py-name">k2</tt><tt class="py-op">]</tt> <tt class="py-op">*</tt> <tt class="py-name">small</tt> <tt class="py-op">*</tt> <tt class="py-name">ten</tt> </tt>
<a name="L124"></a><tt class="py-lineno"> 124</tt>  <tt class="py-line"> </tt>
<a name="L125"></a><tt class="py-lineno"> 125</tt>  <tt class="py-line">        <tt class="py-name">k4</tt><tt class="py-op">,</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-number">1</tt> <tt class="py-op">-</tt> <tt class="py-name">smallE2</tt><tt class="py-op">)</tt><tt class="py-op">.</tt><tt class="py-name">nonzero</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L126"></a><tt class="py-lineno"> 126</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">k4</tt><tt class="py-op">.</tt><tt class="py-name">size</tt> <tt class="py-op">&gt;</tt> <tt class="py-number">0</tt> <tt class="py-op">:</tt> </tt>
<a name="L127"></a><tt class="py-lineno"> 127</tt>  <tt class="py-line">            <tt class="py-name">k3</tt> <tt class="py-op">=</tt> <tt class="py-name">k1</tt><tt class="py-op">[</tt><tt class="py-name">k4</tt><tt class="py-op">]</tt> </tt>
<a name="L128"></a><tt class="py-lineno"> 128</tt>  <tt class="py-line">            <tt class="py-name">result</tt><tt class="py-op">[</tt><tt class="py-name">k3</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">E1</tt><tt class="py-op">[</tt><tt class="py-name">k3</tt><tt class="py-op">]</tt> <tt class="py-op">+</tt> <tt class="py-name">one</tt> <tt class="py-op">/</tt> <tt class="py-name">ss</tt><tt class="py-op">[</tt><tt class="py-name">k4</tt><tt class="py-op">]</tt> </tt>
<a name="L129"></a><tt class="py-lineno"> 129</tt>  <tt class="py-line">            <tt class="py-name">abserr</tt><tt class="py-op">[</tt><tt class="py-name">k3</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">err1</tt><tt class="py-op">[</tt><tt class="py-name">k3</tt><tt class="py-op">]</tt> <tt class="py-op">+</tt> <tt class="py-name">err2</tt><tt class="py-op">[</tt><tt class="py-name">k3</tt><tt class="py-op">]</tt> <tt class="py-op">+</tt> <tt class="py-name">abs</tt><tt class="py-op">(</tt><tt class="py-name">result</tt><tt class="py-op">[</tt><tt class="py-name">k3</tt><tt class="py-op">]</tt> <tt class="py-op">-</tt> <tt class="py-name">E2</tt><tt class="py-op">[</tt><tt class="py-name">k3</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L130"></a><tt class="py-lineno"> 130</tt>  <tt class="py-line"> </tt>
<a name="L131"></a><tt class="py-lineno"> 131</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">result</tt><tt class="py-op">,</tt> <tt class="py-name">abserr</tt> </tt>
</div><a name="L132"></a><tt class="py-lineno"> 132</tt>  <tt class="py-line"><tt class="py-comment">#max(abserr,small)</tt> </tt>
<a name="L133"></a><tt class="py-lineno"> 133</tt>  <tt class="py-line"> </tt>
<a name="vec2mat"></a><div id="vec2mat-def"><a name="L134"></a><tt class="py-lineno"> 134</tt> <a class="py-toggle" href="#" id="vec2mat-toggle" onclick="return toggle('vec2mat');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core-module.html#vec2mat">vec2mat</a><tt class="py-op">(</tt><tt class="py-param">vec</tt><tt class="py-op">,</tt> <tt class="py-param">n</tt><tt class="py-op">,</tt> <tt class="py-param">m</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="vec2mat-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="vec2mat-expanded"><a name="L135"></a><tt class="py-lineno"> 135</tt>  <tt class="py-line">    <tt class="py-docstring">''' forms the matrix M, such that M(i,j) = vec(i+j)</tt> </tt>
<a name="L136"></a><tt class="py-lineno"> 136</tt>  <tt class="py-line"><tt class="py-docstring">    '''</tt> </tt>
<a name="L137"></a><tt class="py-lineno"> 137</tt>  <tt class="py-line">    <tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">,</tt> <tt class="py-name">j</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">ogrid</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">:</tt><tt class="py-name">n</tt><tt class="py-op">,</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt><tt class="py-name">m</tt><tt class="py-op">]</tt> </tt>
<a name="L138"></a><tt class="py-lineno"> 138</tt>  <tt class="py-line">    <tt class="py-name">ind</tt> <tt class="py-op">=</tt> <tt class="py-name">i</tt> <tt class="py-op">+</tt> <tt class="py-name">j</tt> </tt>
<a name="L139"></a><tt class="py-lineno"> 139</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">matrix</tt><tt class="py-op">(</tt><tt class="py-name">vec</tt><tt class="py-op">[</tt><tt class="py-name">ind</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
</div><a name="L140"></a><tt class="py-lineno"> 140</tt>  <tt class="py-line"> </tt>
<a name="L141"></a><tt class="py-lineno"> 141</tt>  <tt class="py-line"> </tt>
<a name="L142"></a><tt class="py-lineno"> 142</tt>  <tt class="py-line"> </tt>
<a name="_Derivative"></a><div id="_Derivative-def"><a name="L143"></a><tt class="py-lineno"> 143</tt> <a class="py-toggle" href="#" id="_Derivative-toggle" onclick="return toggle('_Derivative');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="numdifftools.core._Derivative-class.html">_Derivative</a><tt class="py-op">(</tt><tt class="py-base-class">object</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Derivative-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="_Derivative-expanded"><a name="L144"></a><tt class="py-lineno"> 144</tt>  <tt class="py-line">    <tt class="py-docstring">''' Object holding common variables and methods for the numdifftools</tt> </tt>
<a name="L145"></a><tt class="py-lineno"> 145</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L146"></a><tt class="py-lineno"> 146</tt>  <tt class="py-line"><tt class="py-docstring">    Parameters</tt> </tt>
<a name="L147"></a><tt class="py-lineno"> 147</tt>  <tt class="py-line"><tt class="py-docstring">    ----------</tt> </tt>
<a name="L148"></a><tt class="py-lineno"> 148</tt>  <tt class="py-line"><tt class="py-docstring">    fun : callable</tt> </tt>
<a name="L149"></a><tt class="py-lineno"> 149</tt>  <tt class="py-line"><tt class="py-docstring">        function to differentiate.</tt> </tt>
<a name="L150"></a><tt class="py-lineno"> 150</tt>  <tt class="py-line"><tt class="py-docstring">    n : Integer from 1 to 4 defining derivative order.     (Default 1)</tt> </tt>
<a name="L151"></a><tt class="py-lineno"> 151</tt>  <tt class="py-line"><tt class="py-docstring">    order : Integer from 1 to 4 defining order of basic method used.</tt> </tt>
<a name="L152"></a><tt class="py-lineno"> 152</tt>  <tt class="py-line"><tt class="py-docstring">            For 'central' methods, it must be from the set [2,4]. (Default 2)</tt> </tt>
<a name="L153"></a><tt class="py-lineno"> 153</tt>  <tt class="py-line"><tt class="py-docstring">    method : Method of estimation.  Valid options are:</tt> </tt>
<a name="L154"></a><tt class="py-lineno"> 154</tt>  <tt class="py-line"><tt class="py-docstring">            'central', 'forward' or 'backward'.          (Default 'central')</tt> </tt>
<a name="L155"></a><tt class="py-lineno"> 155</tt>  <tt class="py-line"><tt class="py-docstring">    romberg_terms : Number of Romberg terms used in the extrapolation.</tt> </tt>
<a name="L156"></a><tt class="py-lineno"> 156</tt>  <tt class="py-line"><tt class="py-docstring">            Must be an integer from 0 to 3.                       (Default 2)</tt> </tt>
<a name="L157"></a><tt class="py-lineno"> 157</tt>  <tt class="py-line"><tt class="py-docstring">            Note: 0 disables the Romberg step completely.</tt> </tt>
<a name="L158"></a><tt class="py-lineno"> 158</tt>  <tt class="py-line"><tt class="py-docstring">    step_fix : If not None, it will define the maximum excursion from step_nom</tt> </tt>
<a name="L159"></a><tt class="py-lineno"> 159</tt>  <tt class="py-line"><tt class="py-docstring">                 that is used and prevent the adaptive logic from working.</tt> </tt>
<a name="L160"></a><tt class="py-lineno"> 160</tt>  <tt class="py-line"><tt class="py-docstring">                 This will be considerably faster, but not necessarily</tt> </tt>
<a name="L161"></a><tt class="py-lineno"> 161</tt>  <tt class="py-line"><tt class="py-docstring">                 as accurate as allowing the adaptive logic to run.</tt> </tt>
<a name="L162"></a><tt class="py-lineno"> 162</tt>  <tt class="py-line"><tt class="py-docstring">                (Default: None)</tt> </tt>
<a name="L163"></a><tt class="py-lineno"> 163</tt>  <tt class="py-line"><tt class="py-docstring">    step_max  : Maximum allowed excursion from step_nom as a multiple of it. (Default 4)</tt> </tt>
<a name="L164"></a><tt class="py-lineno"> 164</tt>  <tt class="py-line"><tt class="py-docstring">    step_nom  : Nominal step.                          default maximum(x0, 0.02) </tt> </tt>
<a name="L165"></a><tt class="py-lineno"> 165</tt>  <tt class="py-line"><tt class="py-docstring">    step_ratio: Ratio used between sequential steps in the estimation</tt> </tt>
<a name="L166"></a><tt class="py-lineno"> 166</tt>  <tt class="py-line"><tt class="py-docstring">                 of the derivative (Default 2)</tt> </tt>
<a name="L167"></a><tt class="py-lineno"> 167</tt>  <tt class="py-line"><tt class="py-docstring">            The steps used h_i = step_nom[i]*step_max*step_ratio**(-arange(steps_num))</tt> </tt>
<a name="L168"></a><tt class="py-lineno"> 168</tt>  <tt class="py-line"><tt class="py-docstring">    step_num : integer</tt> </tt>
<a name="L169"></a><tt class="py-lineno"> 169</tt>  <tt class="py-line"><tt class="py-docstring">        if not specified it will be set according to the following rules: </tt> </tt>
<a name="L170"></a><tt class="py-lineno"> 170</tt>  <tt class="py-line"><tt class="py-docstring">            step_num = 26 if step_fix is None</tt> </tt>
<a name="L171"></a><tt class="py-lineno"> 171</tt>  <tt class="py-line"><tt class="py-docstring">            step_num = 3.+ np.ceil(self.n/2.) + self.order + self.romberg_terms +4 otherwise</tt> </tt>
<a name="L172"></a><tt class="py-lineno"> 172</tt>  <tt class="py-line"><tt class="py-docstring">    vectorized : True  - if your function is vectorized.</tt> </tt>
<a name="L173"></a><tt class="py-lineno"> 173</tt>  <tt class="py-line"><tt class="py-docstring">                False - loop over the successive function calls (default).</tt> </tt>
<a name="L174"></a><tt class="py-lineno"> 174</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L175"></a><tt class="py-lineno"> 175</tt>  <tt class="py-line"><tt class="py-docstring">    Uses a semi-adaptive scheme to provide the best estimate of the</tt> </tt>
<a name="L176"></a><tt class="py-lineno"> 176</tt>  <tt class="py-line"><tt class="py-docstring">    derivative by its automatic choice of a differencing interval. It uses</tt> </tt>
<a name="L177"></a><tt class="py-lineno"> 177</tt>  <tt class="py-line"><tt class="py-docstring">    finite difference approximations of various orders, coupled with a</tt> </tt>
<a name="L178"></a><tt class="py-lineno"> 178</tt>  <tt class="py-line"><tt class="py-docstring">    generalized (multiple term) Romberg extrapolation. This also yields the</tt> </tt>
<a name="L179"></a><tt class="py-lineno"> 179</tt>  <tt class="py-line"><tt class="py-docstring">    error estimate provided. See the document DERIVEST.pdf for more explanation</tt> </tt>
<a name="L180"></a><tt class="py-lineno"> 180</tt>  <tt class="py-line"><tt class="py-docstring">    of the algorithms behind the parameters.</tt> </tt>
<a name="L181"></a><tt class="py-lineno"> 181</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L182"></a><tt class="py-lineno"> 182</tt>  <tt class="py-line"><tt class="py-docstring">     Note on order: higher order methods will generally be more accurate,</tt> </tt>
<a name="L183"></a><tt class="py-lineno"> 183</tt>  <tt class="py-line"><tt class="py-docstring">             but may also suffer more from numerical problems. First order</tt> </tt>
<a name="L184"></a><tt class="py-lineno"> 184</tt>  <tt class="py-line"><tt class="py-docstring">             methods would usually not be recommended.</tt> </tt>
<a name="L185"></a><tt class="py-lineno"> 185</tt>  <tt class="py-line"><tt class="py-docstring">     Note on method: Central difference methods are usually the most accurate,</tt> </tt>
<a name="L186"></a><tt class="py-lineno"> 186</tt>  <tt class="py-line"><tt class="py-docstring">            but sometimes one can only allow evaluation in forward or backward</tt> </tt>
<a name="L187"></a><tt class="py-lineno"> 187</tt>  <tt class="py-line"><tt class="py-docstring">            direction.</tt> </tt>
<a name="L188"></a><tt class="py-lineno"> 188</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L189"></a><tt class="py-lineno"> 189</tt>  <tt class="py-line"><tt class="py-docstring">    '''</tt> </tt>
<a name="_Derivative.__init__"></a><div id="_Derivative.__init__-def"><a name="L190"></a><tt class="py-lineno"> 190</tt> <a class="py-toggle" href="#" id="_Derivative.__init__-toggle" onclick="return toggle('_Derivative.__init__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core._Derivative-class.html#__init__">__init__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">fun</tt><tt class="py-op">,</tt> <tt class="py-op">**</tt><tt class="py-param">kwds</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Derivative.__init__-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="_Derivative.__init__-expanded"><a name="L191"></a><tt class="py-lineno"> 191</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">fun</tt> <tt class="py-op">=</tt> <tt class="py-name">fun</tt> </tt>
<a name="L192"></a><tt class="py-lineno"> 192</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">n</tt> <tt class="py-op">=</tt> <tt class="py-number">1</tt> </tt>
<a name="L193"></a><tt class="py-lineno"> 193</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">order</tt> <tt class="py-op">=</tt> <tt class="py-number">2</tt> </tt>
<a name="L194"></a><tt class="py-lineno"> 194</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">method</tt> <tt class="py-op">=</tt> <tt class="py-string">'central'</tt> </tt>
<a name="L195"></a><tt class="py-lineno"> 195</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">romberg_terms</tt> <tt class="py-op">=</tt> <tt class="py-number">2</tt> </tt>
<a name="L196"></a><tt class="py-lineno"> 196</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">step_fix</tt> <tt class="py-op">=</tt> <tt class="py-name">None</tt> </tt>
<a name="L197"></a><tt class="py-lineno"> 197</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">step_max</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-number">2.0</tt> <tt class="py-op">+</tt> <tt class="py-number">1.0</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-number">1.0</tt> </tt>
<a name="L198"></a><tt class="py-lineno"> 198</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">step_ratio</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-number">2.0</tt> <tt class="py-op">+</tt> <tt class="py-number">1.0</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-number">1.0</tt> </tt>
<a name="L199"></a><tt class="py-lineno"> 199</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">step_nom</tt> <tt class="py-op">=</tt> <tt class="py-name">None</tt> </tt>
<a name="L200"></a><tt class="py-lineno"> 200</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">step_num</tt> <tt class="py-op">=</tt> <tt class="py-name">None</tt> </tt>
<a name="L201"></a><tt class="py-lineno"> 201</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">vectorized</tt> <tt class="py-op">=</tt> <tt class="py-name">False</tt> </tt>
<a name="L202"></a><tt class="py-lineno"> 202</tt>  <tt class="py-line"> </tt>
<a name="L203"></a><tt class="py-lineno"> 203</tt>  <tt class="py-line">        <tt class="py-name">valid_keys</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__dict__</tt> </tt>
<a name="L204"></a><tt class="py-lineno"> 204</tt>  <tt class="py-line">        <tt class="py-name">dict2update</tt> <tt class="py-op">=</tt> <tt class="py-name">dict</tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">k</tt><tt class="py-op">,</tt> <tt class="py-name">kwds</tt><tt class="py-op">[</tt><tt class="py-name">k</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt class="py-name">k</tt> <tt class="py-keyword">in</tt> <tt class="py-name">valid_keys</tt> <tt class="py-keyword">if</tt> <tt class="py-name">k</tt> <tt class="py-keyword">in</tt> <tt class="py-name">kwds</tt><tt class="py-op">)</tt> </tt>
<a name="L205"></a><tt class="py-lineno"> 205</tt>  <tt class="py-line"> </tt>
<a name="L206"></a><tt class="py-lineno"> 206</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">any</tt><tt class="py-op">(</tt><tt class="py-name">dict2update</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L207"></a><tt class="py-lineno"> 207</tt>  <tt class="py-line">            <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__dict__</tt><tt class="py-op">.</tt><tt class="py-name">update</tt><tt class="py-op">(</tt><tt class="py-name">dict2update</tt><tt class="py-op">)</tt> </tt>
<a name="L208"></a><tt class="py-lineno"> 208</tt>  <tt class="py-line"> </tt>
<a name="L209"></a><tt class="py-lineno"> 209</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-2" class="py-name" targets="Method numdifftools.core._Derivative._check_params()=numdifftools.core._Derivative-class.html#_check_params"><a title="numdifftools.core._Derivative._check_params" class="py-name" href="#" onclick="return doclink('link-2', '_check_params', 'link-2');">_check_params</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L210"></a><tt class="py-lineno"> 210</tt>  <tt class="py-line"> </tt>
<a name="L211"></a><tt class="py-lineno"> 211</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">error_estimate</tt> <tt class="py-op">=</tt> <tt class="py-name">None</tt> </tt>
<a name="L212"></a><tt class="py-lineno"> 212</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">finaldelta</tt> <tt class="py-op">=</tt> <tt class="py-name">None</tt> </tt>
<a name="L213"></a><tt class="py-lineno"> 213</tt>  <tt class="py-line"> </tt>
<a name="L214"></a><tt class="py-lineno"> 214</tt>  <tt class="py-line">        <tt class="py-comment"># The remaining member variables are set by _initialize</tt> </tt>
<a name="L215"></a><tt class="py-lineno"> 215</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_fda_rule</tt> <tt class="py-op">=</tt> <tt class="py-name">None</tt> </tt>
<a name="L216"></a><tt class="py-lineno"> 216</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_delta</tt> <tt class="py-op">=</tt> <tt class="py-name">None</tt> </tt>
<a name="L217"></a><tt class="py-lineno"> 217</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_rmat</tt> <tt class="py-op">=</tt> <tt class="py-name">None</tt> </tt>
<a name="L218"></a><tt class="py-lineno"> 218</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_qromb</tt> <tt class="py-op">=</tt> <tt class="py-name">None</tt> </tt>
<a name="L219"></a><tt class="py-lineno"> 219</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_rromb</tt> <tt class="py-op">=</tt> <tt class="py-name">None</tt> </tt>
<a name="L220"></a><tt class="py-lineno"> 220</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_fdiff</tt> <tt class="py-op">=</tt> <tt class="py-name">None</tt> </tt>
</div><a name="L221"></a><tt class="py-lineno"> 221</tt>  <tt class="py-line"> </tt>
<a name="L222"></a><tt class="py-lineno"> 222</tt>  <tt class="py-line"> </tt>
<a name="_Derivative._check_params"></a><div id="_Derivative._check_params-def"><a name="L223"></a><tt class="py-lineno"> 223</tt> <a class="py-toggle" href="#" id="_Derivative._check_params-toggle" onclick="return toggle('_Derivative._check_params');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core._Derivative-class.html#_check_params">_check_params</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Derivative._check_params-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="_Derivative._check_params-expanded"><a name="L224"></a><tt class="py-lineno"> 224</tt>  <tt class="py-line">        <tt class="py-docstring">''' check the parameters for acceptability</tt> </tt>
<a name="L225"></a><tt class="py-lineno"> 225</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L226"></a><tt class="py-lineno"> 226</tt>  <tt class="py-line">        <tt class="py-name">atleast_1d</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">atleast_1d</tt> </tt>
<a name="L227"></a><tt class="py-lineno"> 227</tt>  <tt class="py-line">        <tt class="py-name">kwds</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__dict__</tt> </tt>
<a name="L228"></a><tt class="py-lineno"> 228</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-name">name</tt> <tt class="py-keyword">in</tt> <tt class="py-op">[</tt><tt class="py-string">'n'</tt><tt class="py-op">,</tt> <tt class="py-string">'order'</tt><tt class="py-op">]</tt><tt class="py-op">:</tt> </tt>
<a name="L229"></a><tt class="py-lineno"> 229</tt>  <tt class="py-line">            <tt class="py-name">val</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">atleast_1d</tt><tt class="py-op">(</tt><tt class="py-name">kwds</tt><tt class="py-op">[</tt><tt class="py-name">name</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L230"></a><tt class="py-lineno"> 230</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">val</tt><tt class="py-op">)</tt> <tt class="py-op">!=</tt> <tt class="py-number">1</tt><tt class="py-op">)</tt> <tt class="py-keyword">or</tt> <tt class="py-op">(</tt><tt class="py-keyword">not</tt> <tt class="py-name">val</tt> <tt class="py-keyword">in</tt> <tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-number">3</tt><tt class="py-op">,</tt> <tt class="py-number">4</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L231"></a><tt class="py-lineno"> 231</tt>  <tt class="py-line">                <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'%s must be scalar, one of [1 2 3 4].'</tt> <tt class="py-op">%</tt> <tt class="py-name">name</tt><tt class="py-op">)</tt> </tt>
<a name="L232"></a><tt class="py-lineno"> 232</tt>  <tt class="py-line">        <tt class="py-name">name</tt> <tt class="py-op">=</tt> <tt class="py-string">'romberg_terms'</tt> </tt>
<a name="L233"></a><tt class="py-lineno"> 233</tt>  <tt class="py-line">        <tt class="py-name">val</tt> <tt class="py-op">=</tt> <tt class="py-name">atleast_1d</tt><tt class="py-op">(</tt><tt class="py-name">kwds</tt><tt class="py-op">[</tt><tt class="py-name">name</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L234"></a><tt class="py-lineno"> 234</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">val</tt><tt class="py-op">)</tt> <tt class="py-op">!=</tt> <tt class="py-number">1</tt><tt class="py-op">)</tt> <tt class="py-keyword">or</tt> <tt class="py-op">(</tt><tt class="py-keyword">not</tt> <tt class="py-name">val</tt> <tt class="py-keyword">in</tt> <tt class="py-op">(</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-number">3</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L235"></a><tt class="py-lineno"> 235</tt>  <tt class="py-line">            <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'%s must be scalar, one of [0 1 2 3].'</tt> <tt class="py-op">%</tt> <tt class="py-name">name</tt><tt class="py-op">)</tt> </tt>
<a name="L236"></a><tt class="py-lineno"> 236</tt>  <tt class="py-line"> </tt>
<a name="L237"></a><tt class="py-lineno"> 237</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-name">name</tt> <tt class="py-keyword">in</tt> <tt class="py-op">(</tt><tt class="py-string">'step_fix'</tt><tt class="py-op">,</tt> <tt class="py-string">'step_max'</tt><tt class="py-op">,</tt> <tt class="py-string">'step_num'</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L238"></a><tt class="py-lineno"> 238</tt>  <tt class="py-line">            <tt class="py-name">val</tt> <tt class="py-op">=</tt> <tt class="py-name">kwds</tt><tt class="py-op">[</tt><tt class="py-name">name</tt><tt class="py-op">]</tt> </tt>
<a name="L239"></a><tt class="py-lineno"> 239</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt class="py-op">(</tt><tt class="py-name">val</tt> <tt class="py-op">!=</tt> <tt class="py-name">None</tt> <tt class="py-keyword">and</tt> <tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">atleast_1d</tt><tt class="py-op">(</tt><tt class="py-name">val</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> <tt class="py-op">&gt;</tt> <tt class="py-number">1</tt><tt class="py-op">)</tt> <tt class="py-keyword">or</tt> <tt class="py-op">(</tt><tt class="py-name">val</tt> <tt class="py-op">&lt;=</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L240"></a><tt class="py-lineno"> 240</tt>  <tt class="py-line">                <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'%s must be None or a scalar, &gt;0.'</tt> <tt class="py-op">%</tt> <tt class="py-name">name</tt><tt class="py-op">)</tt> </tt>
<a name="L241"></a><tt class="py-lineno"> 241</tt>  <tt class="py-line"> </tt>
<a name="L242"></a><tt class="py-lineno"> 242</tt>  <tt class="py-line">        <tt class="py-name">validMethods</tt> <tt class="py-op">=</tt> <tt class="py-name">dict</tt><tt class="py-op">(</tt><tt class="py-name">c</tt><tt class="py-op">=</tt><tt class="py-string">'central'</tt><tt class="py-op">,</tt> <tt class="py-name">f</tt><tt class="py-op">=</tt><tt class="py-string">'forward'</tt><tt class="py-op">,</tt> <tt class="py-name">b</tt><tt class="py-op">=</tt><tt class="py-string">'backward'</tt><tt class="py-op">)</tt> </tt>
<a name="L243"></a><tt class="py-lineno"> 243</tt>  <tt class="py-line">        <tt class="py-name">method</tt> <tt class="py-op">=</tt> <tt class="py-name">validMethods</tt><tt class="py-op">.</tt><tt class="py-name">get</tt><tt class="py-op">(</tt><tt class="py-name">kwds</tt><tt class="py-op">[</tt><tt class="py-string">'method'</tt><tt class="py-op">]</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L244"></a><tt class="py-lineno"> 244</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">method</tt> <tt class="py-op">==</tt> <tt class="py-name">None</tt> <tt class="py-op">:</tt> </tt>
<a name="L245"></a><tt class="py-lineno"> 245</tt>  <tt class="py-line">            <tt class="py-name">t</tt> <tt class="py-op">=</tt> <tt class="py-string">'Invalid method: Must start with one of c,f,b characters!'</tt> </tt>
<a name="L246"></a><tt class="py-lineno"> 246</tt>  <tt class="py-line">            <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-name">t</tt><tt class="py-op">)</tt> </tt>
<a name="L247"></a><tt class="py-lineno"> 247</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">method</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">==</tt> <tt class="py-string">'c'</tt> <tt class="py-keyword">and</tt> <tt class="py-name">kwds</tt><tt class="py-op">[</tt><tt class="py-string">'method'</tt><tt class="py-op">]</tt> <tt class="py-keyword">in</tt> <tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-number">3</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L248"></a><tt class="py-lineno"> 248</tt>  <tt class="py-line">            <tt class="py-name">t</tt> <tt class="py-op">=</tt> <tt class="py-string">'order 1 or 3 is not possible for central difference methods'</tt> </tt>
<a name="L249"></a><tt class="py-lineno"> 249</tt>  <tt class="py-line">            <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-name">t</tt><tt class="py-op">)</tt> </tt>
</div><a name="L250"></a><tt class="py-lineno"> 250</tt>  <tt class="py-line"> </tt>
<a name="_Derivative._initialize"></a><div id="_Derivative._initialize-def"><a name="L251"></a><tt class="py-lineno"> 251</tt> <a class="py-toggle" href="#" id="_Derivative._initialize-toggle" onclick="return toggle('_Derivative._initialize');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core._Derivative-class.html#_initialize">_initialize</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Derivative._initialize-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="_Derivative._initialize-expanded"><a name="L252"></a><tt class="py-lineno"> 252</tt>  <tt class="py-line">        <tt class="py-docstring">'''Set derivative parameters:</tt> </tt>
<a name="L253"></a><tt class="py-lineno"> 253</tt>  <tt class="py-line"><tt class="py-docstring">            stepsize, differention rule and romberg extrapolation matrices</tt> </tt>
<a name="L254"></a><tt class="py-lineno"> 254</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L255"></a><tt class="py-lineno"> 255</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-3" class="py-name" targets="Method numdifftools.core._Derivative._set_delta()=numdifftools.core._Derivative-class.html#_set_delta"><a title="numdifftools.core._Derivative._set_delta" class="py-name" href="#" onclick="return doclink('link-3', '_set_delta', 'link-3');">_set_delta</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L256"></a><tt class="py-lineno"> 256</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-4" class="py-name" targets="Method numdifftools.core._Derivative._set_fda_rule()=numdifftools.core._Derivative-class.html#_set_fda_rule"><a title="numdifftools.core._Derivative._set_fda_rule" class="py-name" href="#" onclick="return doclink('link-4', '_set_fda_rule', 'link-4');">_set_fda_rule</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L257"></a><tt class="py-lineno"> 257</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-5" class="py-name" targets="Method numdifftools.core._Derivative._set_romb_qr()=numdifftools.core._Derivative-class.html#_set_romb_qr"><a title="numdifftools.core._Derivative._set_romb_qr" class="py-name" href="#" onclick="return doclink('link-5', '_set_romb_qr', 'link-5');">_set_romb_qr</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L258"></a><tt class="py-lineno"> 258</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-6" class="py-name" targets="Method numdifftools.core._Derivative._set_difference_function()=numdifftools.core._Derivative-class.html#_set_difference_function"><a title="numdifftools.core._Derivative._set_difference_function" class="py-name" href="#" onclick="return doclink('link-6', '_set_difference_function', 'link-6');">_set_difference_function</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
</div><a name="L259"></a><tt class="py-lineno"> 259</tt>  <tt class="py-line"> </tt>
<a name="_Derivative._fder"></a><div id="_Derivative._fder-def"><a name="L260"></a><tt class="py-lineno"> 260</tt> <a class="py-toggle" href="#" id="_Derivative._fder-toggle" onclick="return toggle('_Derivative._fder');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core._Derivative-class.html#_fder">_fder</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">fun</tt><tt class="py-op">,</tt> <tt class="py-param">f_x0i</tt><tt class="py-op">,</tt> <tt class="py-param">x0i</tt><tt class="py-op">,</tt> <tt class="py-param">h</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Derivative._fder-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="_Derivative._fder-expanded"><a name="L261"></a><tt class="py-lineno"> 261</tt>  <tt class="py-line">        <tt class="py-docstring">''' Return derivative estimates of f at x0 for a sequence of stepsizes h</tt> </tt>
<a name="L262"></a><tt class="py-lineno"> 262</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L263"></a><tt class="py-lineno"> 263</tt>  <tt class="py-line"><tt class="py-docstring">        Member variables used</tt> </tt>
<a name="L264"></a><tt class="py-lineno"> 264</tt>  <tt class="py-line"><tt class="py-docstring">        ---------------------</tt> </tt>
<a name="L265"></a><tt class="py-lineno"> 265</tt>  <tt class="py-line"><tt class="py-docstring">        n</tt> </tt>
<a name="L266"></a><tt class="py-lineno"> 266</tt>  <tt class="py-line"><tt class="py-docstring">        _fda_rule</tt> </tt>
<a name="L267"></a><tt class="py-lineno"> 267</tt>  <tt class="py-line"><tt class="py-docstring">        romberg_terms</tt> </tt>
<a name="L268"></a><tt class="py-lineno"> 268</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L269"></a><tt class="py-lineno"> 269</tt>  <tt class="py-line">        <tt class="py-name">fdarule</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_fda_rule</tt> </tt>
<a name="L270"></a><tt class="py-lineno"> 270</tt>  <tt class="py-line">        <tt class="py-name">nfda</tt> <tt class="py-op">=</tt> <tt class="py-name">fdarule</tt><tt class="py-op">.</tt><tt class="py-name">size</tt> </tt>
<a name="L271"></a><tt class="py-lineno"> 271</tt>  <tt class="py-line">        <tt class="py-name">ndel</tt> <tt class="py-op">=</tt> <tt class="py-name">h</tt><tt class="py-op">.</tt><tt class="py-name">size</tt> </tt>
<a name="L272"></a><tt class="py-lineno"> 272</tt>  <tt class="py-line"> </tt>
<a name="L273"></a><tt class="py-lineno"> 273</tt>  <tt class="py-line">        <tt class="py-name">f_del</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_fdiff</tt><tt class="py-op">(</tt><tt class="py-name">fun</tt><tt class="py-op">,</tt> <tt class="py-name">f_x0i</tt><tt class="py-op">,</tt> <tt class="py-name">x0i</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt><tt class="py-op">)</tt> </tt>
<a name="L274"></a><tt class="py-lineno"> 274</tt>  <tt class="py-line"> </tt>
<a name="L275"></a><tt class="py-lineno"> 275</tt>  <tt class="py-line">        <tt class="py-comment"># check the size of f_del to ensure it was properly vectorized.</tt> </tt>
<a name="L276"></a><tt class="py-lineno"> 276</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">f_del</tt><tt class="py-op">.</tt><tt class="py-name">size</tt> <tt class="py-op">!=</tt> <tt class="py-name">h</tt><tt class="py-op">.</tt><tt class="py-name">size</tt><tt class="py-op">:</tt> </tt>
<a name="L277"></a><tt class="py-lineno"> 277</tt>  <tt class="py-line">            <tt class="py-name">t</tt> <tt class="py-op">=</tt> <tt class="py-string">'fun did not return data of correct size (it must be vectorized)'</tt> </tt>
<a name="L278"></a><tt class="py-lineno"> 278</tt>  <tt class="py-line">            <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-name">t</tt><tt class="py-op">)</tt> </tt>
<a name="L279"></a><tt class="py-lineno"> 279</tt>  <tt class="py-line"> </tt>
<a name="L280"></a><tt class="py-lineno"> 280</tt>  <tt class="py-line">        <tt class="py-comment"># Apply the finite difference rule at each delta, scaling</tt> </tt>
<a name="L281"></a><tt class="py-lineno"> 281</tt>  <tt class="py-line">        <tt class="py-comment"># as appropriate for delta and the requested DerivativeOrder.</tt> </tt>
<a name="L282"></a><tt class="py-lineno"> 282</tt>  <tt class="py-line">        <tt class="py-comment"># First, decide how many of these estimates we will end up with.</tt> </tt>
<a name="L283"></a><tt class="py-lineno"> 283</tt>  <tt class="py-line">        <tt class="py-name">ne</tt> <tt class="py-op">=</tt> <tt class="py-name">ndel</tt> <tt class="py-op">+</tt> <tt class="py-number">1</tt> <tt class="py-op">-</tt> <tt class="py-name">nfda</tt> <tt class="py-op">-</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">romberg_terms</tt> </tt>
<a name="L284"></a><tt class="py-lineno"> 284</tt>  <tt class="py-line"> </tt>
<a name="L285"></a><tt class="py-lineno"> 285</tt>  <tt class="py-line">        <tt class="py-comment"># Form the initial derivative estimates from the chosen</tt> </tt>
<a name="L286"></a><tt class="py-lineno"> 286</tt>  <tt class="py-line">        <tt class="py-comment"># finite difference method.</tt> </tt>
<a name="L287"></a><tt class="py-lineno"> 287</tt>  <tt class="py-line">        <tt class="py-name">der_init</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">asarray</tt><tt class="py-op">(</tt><tt id="link-7" class="py-name" targets="Function numdifftools.core.vec2mat()=numdifftools.core-module.html#vec2mat"><a title="numdifftools.core.vec2mat" class="py-name" href="#" onclick="return doclink('link-7', 'vec2mat', 'link-7');">vec2mat</a></tt><tt class="py-op">(</tt><tt class="py-name">f_del</tt><tt class="py-op">,</tt> <tt class="py-name">ne</tt><tt class="py-op">,</tt> <tt class="py-name">nfda</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">fdarule</tt><tt class="py-op">.</tt><tt class="py-name">T</tt><tt class="py-op">)</tt> </tt>
<a name="L288"></a><tt class="py-lineno"> 288</tt>  <tt class="py-line"> </tt>
<a name="L289"></a><tt class="py-lineno"> 289</tt>  <tt class="py-line">        <tt class="py-comment"># scale to reflect the local delta</tt> </tt>
<a name="L290"></a><tt class="py-lineno"> 290</tt>  <tt class="py-line">        <tt class="py-name">der_init</tt> <tt class="py-op">=</tt> <tt class="py-name">der_init</tt><tt class="py-op">.</tt><tt class="py-name">ravel</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> <tt class="py-op">/</tt> <tt class="py-op">(</tt><tt class="py-name">h</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">:</tt><tt class="py-name">ne</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> <tt class="py-op">**</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">n</tt> </tt>
<a name="L291"></a><tt class="py-lineno"> 291</tt>  <tt class="py-line"> </tt>
<a name="L292"></a><tt class="py-lineno"> 292</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">der_init</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">:</tt><tt class="py-name">ne</tt><tt class="py-op">]</tt> </tt>
</div><a name="L293"></a><tt class="py-lineno"> 293</tt>  <tt class="py-line">     </tt>
<a name="_Derivative._trim_estimates"></a><div id="_Derivative._trim_estimates-def"><a name="L294"></a><tt class="py-lineno"> 294</tt> <a class="py-toggle" href="#" id="_Derivative._trim_estimates-toggle" onclick="return toggle('_Derivative._trim_estimates');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core._Derivative-class.html#_trim_estimates">_trim_estimates</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">der_romb</tt><tt class="py-op">,</tt> <tt class="py-param">errors</tt><tt class="py-op">,</tt> <tt class="py-param">h</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Derivative._trim_estimates-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="_Derivative._trim_estimates-expanded"><a name="L295"></a><tt class="py-lineno"> 295</tt>  <tt class="py-line">        <tt class="py-docstring">'''</tt> </tt>
<a name="L296"></a><tt class="py-lineno"> 296</tt>  <tt class="py-line"><tt class="py-docstring">        trim off the estimates at each end of the scale if not self.step_fix</tt> </tt>
<a name="L297"></a><tt class="py-lineno"> 297</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L298"></a><tt class="py-lineno"> 298</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">step_fix</tt> <tt class="py-keyword">is</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> </tt>
<a name="L299"></a><tt class="py-lineno"> 299</tt>  <tt class="py-line">            <tt class="py-name">der_romb</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">atleast_1d</tt><tt class="py-op">(</tt><tt class="py-name">der_romb</tt><tt class="py-op">)</tt> </tt>
<a name="L300"></a><tt class="py-lineno"> 300</tt>  <tt class="py-line">            <tt class="py-name">tags</tt><tt class="py-op">,</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">where</tt><tt class="py-op">(</tt><tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">isfinite</tt><tt class="py-op">(</tt><tt class="py-name">der_romb</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L301"></a><tt class="py-lineno"> 301</tt>  <tt class="py-line">            <tt class="py-name">num_vals</tt> <tt class="py-op">=</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">der_romb</tt><tt class="py-op">)</tt> </tt>
<a name="L302"></a><tt class="py-lineno"> 302</tt>  <tt class="py-line">            <tt class="py-comment">#if len(tags) == num_vals:</tt> </tt>
<a name="L303"></a><tt class="py-lineno"> 303</tt>  <tt class="py-line">            <tt class="py-name">nr_rem_min</tt> <tt class="py-op">=</tt> <tt class="py-name">int</tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">num_vals</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-number">2</tt><tt class="py-op">)</tt> </tt>
<a name="L304"></a><tt class="py-lineno"> 304</tt>  <tt class="py-line">            <tt class="py-name">nr_rem</tt> <tt class="py-op">=</tt> <tt class="py-name">min</tt><tt class="py-op">(</tt><tt class="py-number">2</tt> <tt class="py-op">*</tt> <tt class="py-name">max</tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">n</tt> <tt class="py-op">-</tt> <tt class="py-number">1</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-number">1</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">nr_rem_min</tt><tt class="py-op">)</tt> </tt>
<a name="L305"></a><tt class="py-lineno"> 305</tt>  <tt class="py-line">            <tt class="py-name">tags</tt> <tt class="py-op">=</tt> <tt class="py-name">der_romb</tt><tt class="py-op">.</tt><tt class="py-name">argsort</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L306"></a><tt class="py-lineno"> 306</tt>  <tt class="py-line">            <tt class="py-name">tags</tt> <tt class="py-op">=</tt> <tt class="py-name">tags</tt><tt class="py-op">[</tt><tt class="py-name">nr_rem</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-name">nr_rem</tt><tt class="py-op">]</tt> </tt>
<a name="L307"></a><tt class="py-lineno"> 307</tt>  <tt class="py-line">            <tt class="py-name">der_romb</tt> <tt class="py-op">=</tt> <tt class="py-name">der_romb</tt><tt class="py-op">[</tt><tt class="py-name">tags</tt><tt class="py-op">]</tt> </tt>
<a name="L308"></a><tt class="py-lineno"> 308</tt>  <tt class="py-line">            <tt class="py-name">errors</tt> <tt class="py-op">=</tt> <tt class="py-name">errors</tt><tt class="py-op">[</tt><tt class="py-name">tags</tt><tt class="py-op">]</tt> </tt>
<a name="L309"></a><tt class="py-lineno"> 309</tt>  <tt class="py-line">            <tt class="py-name">trimdelta</tt> <tt class="py-op">=</tt> <tt class="py-name">h</tt><tt class="py-op">[</tt><tt class="py-name">tags</tt><tt class="py-op">]</tt> </tt>
<a name="L310"></a><tt class="py-lineno"> 310</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L311"></a><tt class="py-lineno"> 311</tt>  <tt class="py-line">            <tt class="py-name">trimdelta</tt> <tt class="py-op">=</tt> <tt class="py-name">h</tt> </tt>
<a name="L312"></a><tt class="py-lineno"> 312</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">der_romb</tt><tt class="py-op">,</tt> <tt class="py-name">errors</tt><tt class="py-op">,</tt> <tt class="py-name">trimdelta</tt> </tt>
</div><a name="L313"></a><tt class="py-lineno"> 313</tt>  <tt class="py-line"> </tt>
<a name="_Derivative._derivative"></a><div id="_Derivative._derivative-def"><a name="L314"></a><tt class="py-lineno"> 314</tt> <a class="py-toggle" href="#" id="_Derivative._derivative-toggle" onclick="return toggle('_Derivative._derivative');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core._Derivative-class.html#_derivative">_derivative</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">fun</tt><tt class="py-op">,</tt> <tt class="py-param">x00</tt><tt class="py-op">,</tt> <tt class="py-param">stepNom</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Derivative._derivative-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="_Derivative._derivative-expanded"><a name="L315"></a><tt class="py-lineno"> 315</tt>  <tt class="py-line">        <tt class="py-name">x0</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">atleast_1d</tt><tt class="py-op">(</tt><tt class="py-name">x00</tt><tt class="py-op">)</tt> </tt>
<a name="L316"></a><tt class="py-lineno"> 316</tt>  <tt class="py-line"> </tt>
<a name="L317"></a><tt class="py-lineno"> 317</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">stepNom</tt> <tt class="py-keyword">is</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> </tt>
<a name="L318"></a><tt class="py-lineno"> 318</tt>  <tt class="py-line">            <tt class="py-name">stepNom</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">maximum</tt><tt class="py-op">(</tt><tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">abs</tt><tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-number">0.02</tt><tt class="py-op">)</tt> </tt>
<a name="L319"></a><tt class="py-lineno"> 319</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L320"></a><tt class="py-lineno"> 320</tt>  <tt class="py-line">            <tt class="py-name">stepNom</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">atleast_1d</tt><tt class="py-op">(</tt><tt class="py-name">stepNom</tt><tt class="py-op">)</tt> </tt>
<a name="L321"></a><tt class="py-lineno"> 321</tt>  <tt class="py-line">         </tt>
<a name="L322"></a><tt class="py-lineno"> 322</tt>  <tt class="py-line">        <tt class="py-comment"># was a single point supplied?</tt> </tt>
<a name="L323"></a><tt class="py-lineno"> 323</tt>  <tt class="py-line">        <tt class="py-name">nx0</tt> <tt class="py-op">=</tt> <tt class="py-name">x0</tt><tt class="py-op">.</tt><tt class="py-name">shape</tt> </tt>
<a name="L324"></a><tt class="py-lineno"> 324</tt>  <tt class="py-line">        <tt class="py-name">n</tt> <tt class="py-op">=</tt> <tt class="py-name">x0</tt><tt class="py-op">.</tt><tt class="py-name">size</tt> </tt>
<a name="L325"></a><tt class="py-lineno"> 325</tt>  <tt class="py-line"> </tt>
<a name="L326"></a><tt class="py-lineno"> 326</tt>  <tt class="py-line">        <tt class="py-name">f_x0</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-name">nx0</tt><tt class="py-op">)</tt> </tt>
<a name="L327"></a><tt class="py-lineno"> 327</tt>  <tt class="py-line">        <tt class="py-comment"># will we need fun(x0)?</tt> </tt>
<a name="L328"></a><tt class="py-lineno"> 328</tt>  <tt class="py-line">        <tt class="py-name">evenOrder</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">remainder</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">n</tt><tt class="py-op">,</tt> <tt class="py-number">2</tt><tt class="py-op">)</tt> <tt class="py-op">==</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt> </tt>
<a name="L329"></a><tt class="py-lineno"> 329</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt>  <tt class="py-name">evenOrder</tt> <tt class="py-keyword">or</tt> <tt class="py-keyword">not</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">method</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">==</tt> <tt class="py-string">'c'</tt><tt class="py-op">:</tt> </tt>
<a name="L330"></a><tt class="py-lineno"> 330</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">vectorized</tt><tt class="py-op">:</tt> </tt>
<a name="L331"></a><tt class="py-lineno"> 331</tt>  <tt class="py-line">                <tt class="py-name">f_x0</tt> <tt class="py-op">=</tt> <tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">)</tt> </tt>
<a name="L332"></a><tt class="py-lineno"> 332</tt>  <tt class="py-line">            <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L333"></a><tt class="py-lineno"> 333</tt>  <tt class="py-line">                <tt class="py-name">f_x0</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">asfarray</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">x0j</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt class="py-name">x0j</tt> <tt class="py-keyword">in</tt> <tt class="py-name">x0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L334"></a><tt class="py-lineno"> 334</tt>  <tt class="py-line"> </tt>
<a name="L335"></a><tt class="py-lineno"> 335</tt>  <tt class="py-line">        <tt class="py-comment"># Loop over the elements of x0, reducing it to</tt> </tt>
<a name="L336"></a><tt class="py-lineno"> 336</tt>  <tt class="py-line">        <tt class="py-comment"># a scalar problem. Sorry, vectorization is not</tt> </tt>
<a name="L337"></a><tt class="py-lineno"> 337</tt>  <tt class="py-line">        <tt class="py-comment"># complete here, but this IS only a single loop.</tt> </tt>
<a name="L338"></a><tt class="py-lineno"> 338</tt>  <tt class="py-line">        <tt class="py-name">der</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-name">nx0</tt><tt class="py-op">)</tt> </tt>
<a name="L339"></a><tt class="py-lineno"> 339</tt>  <tt class="py-line">        <tt class="py-name">errest</tt> <tt class="py-op">=</tt> <tt class="py-name">der</tt><tt class="py-op">.</tt><tt class="py-name">copy</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L340"></a><tt class="py-lineno"> 340</tt>  <tt class="py-line">        <tt class="py-name">finaldelta</tt> <tt class="py-op">=</tt> <tt class="py-name">der</tt><tt class="py-op">.</tt><tt class="py-name">copy</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L341"></a><tt class="py-lineno"> 341</tt>  <tt class="py-line">        <tt class="py-name">delta</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_delta</tt> </tt>
<a name="L342"></a><tt class="py-lineno"> 342</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-name">i</tt> <tt class="py-keyword">in</tt> <tt class="py-name">range</tt><tt class="py-op">(</tt><tt class="py-name">n</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L343"></a><tt class="py-lineno"> 343</tt>  <tt class="py-line">            <tt class="py-name">f_x0i</tt> <tt class="py-op">=</tt> <tt class="py-name">float</tt><tt class="py-op">(</tt><tt class="py-name">f_x0</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L344"></a><tt class="py-lineno"> 344</tt>  <tt class="py-line">            <tt class="py-name">x0i</tt> <tt class="py-op">=</tt> <tt class="py-name">float</tt><tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L345"></a><tt class="py-lineno"> 345</tt>  <tt class="py-line">            <tt class="py-name">h</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-number">1.0</tt> <tt class="py-op">*</tt> <tt class="py-name">stepNom</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">delta</tt> </tt>
<a name="L346"></a><tt class="py-lineno"> 346</tt>  <tt class="py-line"> </tt>
<a name="L347"></a><tt class="py-lineno"> 347</tt>  <tt class="py-line">            <tt class="py-name">der_init</tt><tt class="py-op">,</tt> <tt class="py-name">h1</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-8" class="py-name" targets="Method numdifftools.core._Derivative._fder()=numdifftools.core._Derivative-class.html#_fder"><a title="numdifftools.core._Derivative._fder" class="py-name" href="#" onclick="return doclink('link-8', '_fder', 'link-8');">_fder</a></tt><tt class="py-op">(</tt><tt class="py-name">fun</tt><tt class="py-op">,</tt> <tt class="py-name">f_x0i</tt><tt class="py-op">,</tt> <tt class="py-name">x0i</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt><tt class="py-op">)</tt> </tt>
<a name="L348"></a><tt class="py-lineno"> 348</tt>  <tt class="py-line"> </tt>
<a name="L349"></a><tt class="py-lineno"> 349</tt>  <tt class="py-line">            <tt class="py-comment"># Each approximation that results is an approximation</tt> </tt>
<a name="L350"></a><tt class="py-lineno"> 350</tt>  <tt class="py-line">            <tt class="py-comment"># of order n to the desired derivative.</tt> </tt>
<a name="L351"></a><tt class="py-lineno"> 351</tt>  <tt class="py-line">            <tt class="py-comment"># Additional (higher order, even or odd) terms in the</tt> </tt>
<a name="L352"></a><tt class="py-lineno"> 352</tt>  <tt class="py-line">            <tt class="py-comment"># Taylor series also remain. Use a generalized (multi-term)</tt> </tt>
<a name="L353"></a><tt class="py-lineno"> 353</tt>  <tt class="py-line">            <tt class="py-comment"># Romberg extrapolation to improve these estimates.</tt> </tt>
<a name="L354"></a><tt class="py-lineno"> 354</tt>  <tt class="py-line">            <tt class="py-name">der_romb</tt><tt class="py-op">,</tt> <tt class="py-name">errors</tt><tt class="py-op">,</tt> <tt class="py-name">h2</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-9" class="py-name" targets="Method numdifftools.core._Derivative._romb_extrap()=numdifftools.core._Derivative-class.html#_romb_extrap"><a title="numdifftools.core._Derivative._romb_extrap" class="py-name" href="#" onclick="return doclink('link-9', '_romb_extrap', 'link-9');">_romb_extrap</a></tt><tt class="py-op">(</tt><tt class="py-name">der_init</tt><tt class="py-op">,</tt> <tt class="py-name">h1</tt><tt class="py-op">)</tt> </tt>
<a name="L355"></a><tt class="py-lineno"> 355</tt>  <tt class="py-line"><tt class="py-comment">#            import matplotlib.pyplot as plt</tt> </tt>
<a name="L356"></a><tt class="py-lineno"> 356</tt>  <tt class="py-line"><tt class="py-comment">#            plt.ioff()</tt> </tt>
<a name="L357"></a><tt class="py-lineno"> 357</tt>  <tt class="py-line"><tt class="py-comment">#            #plt.loglog(h2,der_romb, h2, der_romb+errors,'r--',h2, der_romb-errors,'r--')</tt> </tt>
<a name="L358"></a><tt class="py-lineno"> 358</tt>  <tt class="py-line"><tt class="py-comment">#            plt.loglog(h2,errors,'r--', h2,errors,'r.')</tt> </tt>
<a name="L359"></a><tt class="py-lineno"> 359</tt>  <tt class="py-line"><tt class="py-comment">#            small = np.sqrt(_EPS)**(1./np.sqrt(self.n))</tt> </tt>
<a name="L360"></a><tt class="py-lineno"> 360</tt>  <tt class="py-line"><tt class="py-comment">#            plt.vlines(small, 1e-15, 1)</tt> </tt>
<a name="L361"></a><tt class="py-lineno"> 361</tt>  <tt class="py-line"><tt class="py-comment">#            plt.title('Relative error as function of stepsize nom=%g' % step_nom[i])</tt> </tt>
<a name="L362"></a><tt class="py-lineno"> 362</tt>  <tt class="py-line"><tt class="py-comment">#            print np.vstack((h2,der_romb,errors)).T </tt> </tt>
<a name="L363"></a><tt class="py-lineno"> 363</tt>  <tt class="py-line"><tt class="py-comment">#            plt.show()</tt> </tt>
<a name="L364"></a><tt class="py-lineno"> 364</tt>  <tt class="py-line">            <tt class="py-name">der_romb</tt><tt class="py-op">,</tt> <tt class="py-name">errors</tt><tt class="py-op">,</tt> <tt class="py-name">trimdelta</tt>  <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-10" class="py-name" targets="Method numdifftools.core._Derivative._trim_estimates()=numdifftools.core._Derivative-class.html#_trim_estimates"><a title="numdifftools.core._Derivative._trim_estimates" class="py-name" href="#" onclick="return doclink('link-10', '_trim_estimates', 'link-10');">_trim_estimates</a></tt><tt class="py-op">(</tt><tt class="py-name">der_romb</tt><tt class="py-op">,</tt> <tt class="py-name">errors</tt><tt class="py-op">,</tt> <tt class="py-name">h2</tt><tt class="py-op">)</tt> </tt>
<a name="L365"></a><tt class="py-lineno"> 365</tt>  <tt class="py-line">             </tt>
<a name="L366"></a><tt class="py-lineno"> 366</tt>  <tt class="py-line">            <tt class="py-name">ind</tt> <tt class="py-op">=</tt> <tt class="py-name">errors</tt><tt class="py-op">.</tt><tt class="py-name">argmin</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L367"></a><tt class="py-lineno"> 367</tt>  <tt class="py-line">             </tt>
<a name="L368"></a><tt class="py-lineno"> 368</tt>  <tt class="py-line">            <tt class="py-name">errest</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">errors</tt><tt class="py-op">[</tt><tt class="py-name">ind</tt><tt class="py-op">]</tt> </tt>
<a name="L369"></a><tt class="py-lineno"> 369</tt>  <tt class="py-line">            <tt class="py-name">finaldelta</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">trimdelta</tt><tt class="py-op">[</tt><tt class="py-name">ind</tt><tt class="py-op">]</tt> </tt>
<a name="L370"></a><tt class="py-lineno"> 370</tt>  <tt class="py-line">            <tt class="py-name">der</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">der_romb</tt><tt class="py-op">[</tt><tt class="py-name">ind</tt><tt class="py-op">]</tt> </tt>
<a name="L371"></a><tt class="py-lineno"> 371</tt>  <tt class="py-line"> </tt>
<a name="L372"></a><tt class="py-lineno"> 372</tt>  <tt class="py-line">        <tt class="py-comment"># Save errorEstimate and final step</tt> </tt>
<a name="L373"></a><tt class="py-lineno"> 373</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">error_estimate</tt> <tt class="py-op">=</tt> <tt class="py-name">errest</tt> </tt>
<a name="L374"></a><tt class="py-lineno"> 374</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">finaldelta</tt> <tt class="py-op">=</tt> <tt class="py-name">finaldelta</tt> </tt>
<a name="L375"></a><tt class="py-lineno"> 375</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">der</tt> </tt>
</div><a name="L376"></a><tt class="py-lineno"> 376</tt>  <tt class="py-line">         </tt>
<a name="_Derivative._fda_mat"></a><div id="_Derivative._fda_mat-def"><a name="L377"></a><tt class="py-lineno"> 377</tt> <a class="py-toggle" href="#" id="_Derivative._fda_mat-toggle" onclick="return toggle('_Derivative._fda_mat');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core._Derivative-class.html#_fda_mat">_fda_mat</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">parity</tt><tt class="py-op">,</tt> <tt class="py-param">nterms</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Derivative._fda_mat-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="_Derivative._fda_mat-expanded"><a name="L378"></a><tt class="py-lineno"> 378</tt>  <tt class="py-line">        <tt class="py-docstring">''' Return matrix for fda derivation.</tt> </tt>
<a name="L379"></a><tt class="py-lineno"> 379</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L380"></a><tt class="py-lineno"> 380</tt>  <tt class="py-line"><tt class="py-docstring">        Parameters</tt> </tt>
<a name="L381"></a><tt class="py-lineno"> 381</tt>  <tt class="py-line"><tt class="py-docstring">        ----------</tt> </tt>
<a name="L382"></a><tt class="py-lineno"> 382</tt>  <tt class="py-line"><tt class="py-docstring">        parity : scalar, integer</tt> </tt>
<a name="L383"></a><tt class="py-lineno"> 383</tt>  <tt class="py-line"><tt class="py-docstring">            0 (one sided, all terms included but zeroth order)</tt> </tt>
<a name="L384"></a><tt class="py-lineno"> 384</tt>  <tt class="py-line"><tt class="py-docstring">            1 (only odd terms included)</tt> </tt>
<a name="L385"></a><tt class="py-lineno"> 385</tt>  <tt class="py-line"><tt class="py-docstring">            2 (only even terms included)</tt> </tt>
<a name="L386"></a><tt class="py-lineno"> 386</tt>  <tt class="py-line"><tt class="py-docstring">        nterms : scalar, integer</tt> </tt>
<a name="L387"></a><tt class="py-lineno"> 387</tt>  <tt class="py-line"><tt class="py-docstring">            number of terms</tt> </tt>
<a name="L388"></a><tt class="py-lineno"> 388</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L389"></a><tt class="py-lineno"> 389</tt>  <tt class="py-line"><tt class="py-docstring">        Member variables used</tt> </tt>
<a name="L390"></a><tt class="py-lineno"> 390</tt>  <tt class="py-line"><tt class="py-docstring">        ---------------------</tt> </tt>
<a name="L391"></a><tt class="py-lineno"> 391</tt>  <tt class="py-line"><tt class="py-docstring">        step_ratio</tt> </tt>
<a name="L392"></a><tt class="py-lineno"> 392</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L393"></a><tt class="py-lineno"> 393</tt>  <tt class="py-line">        <tt class="py-comment"># sr is the ratio between successive steps</tt> </tt>
<a name="L394"></a><tt class="py-lineno"> 394</tt>  <tt class="py-line">        <tt class="py-name">srinv</tt> <tt class="py-op">=</tt> <tt class="py-number">1.0</tt> <tt class="py-op">/</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">step_ratio</tt> </tt>
<a name="L395"></a><tt class="py-lineno"> 395</tt>  <tt class="py-line">        <tt class="py-name">factorial</tt> <tt class="py-op">=</tt> <tt class="py-name">misc</tt><tt class="py-op">.</tt><tt class="py-name">factorial</tt> </tt>
<a name="L396"></a><tt class="py-lineno"> 396</tt>  <tt class="py-line">        <tt class="py-name">arange</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">arange</tt> </tt>
<a name="L397"></a><tt class="py-lineno"> 397</tt>  <tt class="py-line">        <tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">,</tt> <tt class="py-name">j</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">ogrid</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">:</tt><tt class="py-name">nterms</tt><tt class="py-op">,</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt><tt class="py-name">nterms</tt><tt class="py-op">]</tt> </tt>
<a name="L398"></a><tt class="py-lineno"> 398</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">parity</tt> <tt class="py-op">==</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L399"></a><tt class="py-lineno"> 399</tt>  <tt class="py-line">            <tt class="py-comment">#% single sided rule</tt> </tt>
<a name="L400"></a><tt class="py-lineno"> 400</tt>  <tt class="py-line">            <tt class="py-name">c</tt> <tt class="py-op">=</tt> <tt class="py-number">1.0</tt> <tt class="py-op">/</tt> <tt class="py-name">factorial</tt><tt class="py-op">(</tt><tt class="py-name">arange</tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-name">nterms</tt> <tt class="py-op">+</tt> <tt class="py-number">1</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L401"></a><tt class="py-lineno"> 401</tt>  <tt class="py-line">            <tt class="py-name">mat</tt> <tt class="py-op">=</tt> <tt class="py-name">c</tt><tt class="py-op">[</tt><tt class="py-name">j</tt><tt class="py-op">]</tt> <tt class="py-op">*</tt> <tt class="py-name">srinv</tt> <tt class="py-op">**</tt> <tt class="py-op">(</tt><tt class="py-name">i</tt> <tt class="py-op">*</tt> <tt class="py-op">(</tt><tt class="py-name">j</tt> <tt class="py-op">+</tt> <tt class="py-number">1</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L402"></a><tt class="py-lineno"> 402</tt>  <tt class="py-line">        <tt class="py-keyword">elif</tt> <tt class="py-name">parity</tt> <tt class="py-op">==</tt> <tt class="py-number">1</tt>  <tt class="py-keyword">or</tt> <tt class="py-name">parity</tt> <tt class="py-op">==</tt> <tt class="py-number">2</tt><tt class="py-op">:</tt> </tt>
<a name="L403"></a><tt class="py-lineno"> 403</tt>  <tt class="py-line">            <tt class="py-name">c</tt> <tt class="py-op">=</tt> <tt class="py-number">1.0</tt> <tt class="py-op">/</tt> <tt class="py-name">factorial</tt><tt class="py-op">(</tt><tt class="py-name">arange</tt><tt class="py-op">(</tt><tt class="py-name">parity</tt><tt class="py-op">,</tt> <tt class="py-number">2</tt> <tt class="py-op">*</tt> <tt class="py-name">nterms</tt> <tt class="py-op">+</tt> <tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-number">2</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L404"></a><tt class="py-lineno"> 404</tt>  <tt class="py-line">            <tt class="py-name">mat</tt> <tt class="py-op">=</tt> <tt class="py-name">c</tt><tt class="py-op">[</tt><tt class="py-name">j</tt><tt class="py-op">]</tt> <tt class="py-op">*</tt> <tt class="py-name">srinv</tt> <tt class="py-op">**</tt> <tt class="py-op">(</tt><tt class="py-name">i</tt> <tt class="py-op">*</tt> <tt class="py-op">(</tt><tt class="py-number">2</tt> <tt class="py-op">*</tt> <tt class="py-name">j</tt> <tt class="py-op">+</tt> <tt class="py-name">parity</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L405"></a><tt class="py-lineno"> 405</tt>  <tt class="py-line"><tt class="py-comment">#        elif parity == 2:</tt> </tt>
<a name="L406"></a><tt class="py-lineno"> 406</tt>  <tt class="py-line"><tt class="py-comment">#            c = 1.0 / factorial(arange(2, 2 * nterms + 1, 2))</tt> </tt>
<a name="L407"></a><tt class="py-lineno"> 407</tt>  <tt class="py-line"><tt class="py-comment">#            mat = c[j] * srinv ** (i * (2 * j + 2))</tt> </tt>
<a name="L408"></a><tt class="py-lineno"> 408</tt>  <tt class="py-line"> </tt>
<a name="L409"></a><tt class="py-lineno"> 409</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">matrix</tt><tt class="py-op">(</tt><tt class="py-name">mat</tt><tt class="py-op">)</tt> </tt>
</div><a name="L410"></a><tt class="py-lineno"> 410</tt>  <tt class="py-line"> </tt>
<a name="L411"></a><tt class="py-lineno"> 411</tt>  <tt class="py-line"> </tt>
<a name="_Derivative._set_fda_rule"></a><div id="_Derivative._set_fda_rule-def"><a name="L412"></a><tt class="py-lineno"> 412</tt> <a class="py-toggle" href="#" id="_Derivative._set_fda_rule-toggle" onclick="return toggle('_Derivative._set_fda_rule');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core._Derivative-class.html#_set_fda_rule">_set_fda_rule</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Derivative._set_fda_rule-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="_Derivative._set_fda_rule-expanded"><a name="L413"></a><tt class="py-lineno"> 413</tt>  <tt class="py-line">        <tt class="py-docstring">'''</tt> </tt>
<a name="L414"></a><tt class="py-lineno"> 414</tt>  <tt class="py-line"><tt class="py-docstring">        Generate finite differencing rule in advance.</tt> </tt>
<a name="L415"></a><tt class="py-lineno"> 415</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L416"></a><tt class="py-lineno"> 416</tt>  <tt class="py-line"><tt class="py-docstring">        The rule is for a nominal unit step size, and will</tt> </tt>
<a name="L417"></a><tt class="py-lineno"> 417</tt>  <tt class="py-line"><tt class="py-docstring">        be scaled later to reflect the local step size.</tt> </tt>
<a name="L418"></a><tt class="py-lineno"> 418</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L419"></a><tt class="py-lineno"> 419</tt>  <tt class="py-line"><tt class="py-docstring">        Member methods used</tt> </tt>
<a name="L420"></a><tt class="py-lineno"> 420</tt>  <tt class="py-line"><tt class="py-docstring">        -------------------</tt> </tt>
<a name="L421"></a><tt class="py-lineno"> 421</tt>  <tt class="py-line"><tt class="py-docstring">        _fda_mat</tt> </tt>
<a name="L422"></a><tt class="py-lineno"> 422</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L423"></a><tt class="py-lineno"> 423</tt>  <tt class="py-line"><tt class="py-docstring">        Member variables used</tt> </tt>
<a name="L424"></a><tt class="py-lineno"> 424</tt>  <tt class="py-line"><tt class="py-docstring">        ---------------------</tt> </tt>
<a name="L425"></a><tt class="py-lineno"> 425</tt>  <tt class="py-line"><tt class="py-docstring">        n</tt> </tt>
<a name="L426"></a><tt class="py-lineno"> 426</tt>  <tt class="py-line"><tt class="py-docstring">        order</tt> </tt>
<a name="L427"></a><tt class="py-lineno"> 427</tt>  <tt class="py-line"><tt class="py-docstring">        method</tt> </tt>
<a name="L428"></a><tt class="py-lineno"> 428</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L429"></a><tt class="py-lineno"> 429</tt>  <tt class="py-line">        <tt class="py-name">derOrder</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">n</tt> </tt>
<a name="L430"></a><tt class="py-lineno"> 430</tt>  <tt class="py-line">        <tt class="py-name">metOrder</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">order</tt> </tt>
<a name="L431"></a><tt class="py-lineno"> 431</tt>  <tt class="py-line">        <tt class="py-name">method</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">method</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> </tt>
<a name="L432"></a><tt class="py-lineno"> 432</tt>  <tt class="py-line">         </tt>
<a name="L433"></a><tt class="py-lineno"> 433</tt>  <tt class="py-line">        <tt class="py-name">matrix</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">matrix</tt> </tt>
<a name="L434"></a><tt class="py-lineno"> 434</tt>  <tt class="py-line">        <tt class="py-name">zeros</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt> </tt>
<a name="L435"></a><tt class="py-lineno"> 435</tt>  <tt class="py-line">        <tt class="py-name">fda_rule</tt> <tt class="py-op">=</tt> <tt class="py-name">matrix</tt><tt class="py-op">(</tt><tt class="py-name">derOrder</tt><tt class="py-op">)</tt> </tt>
<a name="L436"></a><tt class="py-lineno"> 436</tt>  <tt class="py-line">        <tt class="py-comment">#lstsq = linalg.lstsq</tt> </tt>
<a name="L437"></a><tt class="py-lineno"> 437</tt>  <tt class="py-line">        <tt class="py-name">pinv</tt> <tt class="py-op">=</tt> <tt class="py-name">linalg</tt><tt class="py-op">.</tt><tt class="py-name">pinv</tt> </tt>
<a name="L438"></a><tt class="py-lineno"> 438</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">method</tt> <tt class="py-op">==</tt> <tt class="py-string">'c'</tt> <tt class="py-op">:</tt> </tt>
<a name="L439"></a><tt class="py-lineno"> 439</tt>  <tt class="py-line">            <tt class="py-comment">#'central'</tt> </tt>
<a name="L440"></a><tt class="py-lineno"> 440</tt>  <tt class="py-line">            <tt class="py-comment">#for central rules, we will reduce the load by an</tt> </tt>
<a name="L441"></a><tt class="py-lineno"> 441</tt>  <tt class="py-line">            <tt class="py-comment">#even or odd transformation as appropriate.</tt> </tt>
<a name="L442"></a><tt class="py-lineno"> 442</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt class="py-name">metOrder</tt> <tt class="py-op">==</tt> <tt class="py-number">2</tt><tt class="py-op">:</tt> </tt>
<a name="L443"></a><tt class="py-lineno"> 443</tt>  <tt class="py-line">                <tt class="py-keyword">if</tt> <tt class="py-name">derOrder</tt> <tt class="py-op">==</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt> </tt>
<a name="L444"></a><tt class="py-lineno"> 444</tt>  <tt class="py-line">                    <tt class="py-comment"># the odd transformation did all the work</tt> </tt>
<a name="L445"></a><tt class="py-lineno"> 445</tt>  <tt class="py-line">                    <tt class="py-comment">#fda_rule[0] = 1</tt> </tt>
<a name="L446"></a><tt class="py-lineno"> 446</tt>  <tt class="py-line">                    <tt class="py-keyword">pass</tt> </tt>
<a name="L447"></a><tt class="py-lineno"> 447</tt>  <tt class="py-line">                <tt class="py-keyword">elif</tt> <tt class="py-name">derOrder</tt> <tt class="py-op">==</tt> <tt class="py-number">2</tt><tt class="py-op">:</tt> </tt>
<a name="L448"></a><tt class="py-lineno"> 448</tt>  <tt class="py-line">                    <tt class="py-comment"># the even transformation did all the work</tt> </tt>
<a name="L449"></a><tt class="py-lineno"> 449</tt>  <tt class="py-line">                    <tt class="py-comment">#fda_rule[0] = 2</tt> </tt>
<a name="L450"></a><tt class="py-lineno"> 450</tt>  <tt class="py-line">                    <tt class="py-keyword">pass</tt> </tt>
<a name="L451"></a><tt class="py-lineno"> 451</tt>  <tt class="py-line">                <tt class="py-keyword">elif</tt> <tt class="py-name">derOrder</tt> <tt class="py-op">==</tt> <tt class="py-number">3</tt><tt class="py-op">:</tt> </tt>
<a name="L452"></a><tt class="py-lineno"> 452</tt>  <tt class="py-line">                    <tt class="py-comment"># the odd transformation did most of the work, but</tt> </tt>
<a name="L453"></a><tt class="py-lineno"> 453</tt>  <tt class="py-line">                    <tt class="py-comment"># we need to kill off the linear term</tt> </tt>
<a name="L454"></a><tt class="py-lineno"> 454</tt>  <tt class="py-line">                    <tt class="py-name">fda_rule</tt> <tt class="py-op">=</tt> <tt class="py-name">matrix</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">pinv</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-11" class="py-name" targets="Method numdifftools.core._Derivative._fda_mat()=numdifftools.core._Derivative-class.html#_fda_mat"><a title="numdifftools.core._Derivative._fda_mat" class="py-name" href="#" onclick="return doclink('link-11', '_fda_mat', 'link-11');">_fda_mat</a></tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-number">2</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L455"></a><tt class="py-lineno"> 455</tt>  <tt class="py-line">                <tt class="py-keyword">elif</tt> <tt class="py-name">derOrder</tt> <tt class="py-op">==</tt> <tt class="py-number">4</tt><tt class="py-op">:</tt> </tt>
<a name="L456"></a><tt class="py-lineno"> 456</tt>  <tt class="py-line">                    <tt class="py-comment"># the even transformation did most of the work, but</tt> </tt>
<a name="L457"></a><tt class="py-lineno"> 457</tt>  <tt class="py-line">                    <tt class="py-comment"># we need to kill off the quadratic term</tt> </tt>
<a name="L458"></a><tt class="py-lineno"> 458</tt>  <tt class="py-line">                    <tt class="py-name">fda_rule</tt> <tt class="py-op">=</tt> <tt class="py-name">matrix</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">pinv</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-12" class="py-name"><a title="numdifftools.core._Derivative._fda_mat" class="py-name" href="#" onclick="return doclink('link-12', '_fda_mat', 'link-11');">_fda_mat</a></tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-number">2</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L459"></a><tt class="py-lineno"> 459</tt>  <tt class="py-line">            <tt class="py-comment"># a 4th order method. We've already ruled out the 1st</tt> </tt>
<a name="L460"></a><tt class="py-lineno"> 460</tt>  <tt class="py-line">            <tt class="py-comment"># order methods since these are central rules.</tt> </tt>
<a name="L461"></a><tt class="py-lineno"> 461</tt>  <tt class="py-line">            <tt class="py-keyword">elif</tt> <tt class="py-name">derOrder</tt> <tt class="py-op">==</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt> </tt>
<a name="L462"></a><tt class="py-lineno"> 462</tt>  <tt class="py-line">                <tt class="py-comment"># the odd transformation did most of the work, but</tt> </tt>
<a name="L463"></a><tt class="py-lineno"> 463</tt>  <tt class="py-line">                <tt class="py-comment"># we need to kill off the cubic term</tt> </tt>
<a name="L464"></a><tt class="py-lineno"> 464</tt>  <tt class="py-line">                <tt class="py-name">fda_rule</tt> <tt class="py-op">=</tt> <tt class="py-name">matrix</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">pinv</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-13" class="py-name"><a title="numdifftools.core._Derivative._fda_mat" class="py-name" href="#" onclick="return doclink('link-13', '_fda_mat', 'link-11');">_fda_mat</a></tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-number">2</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L465"></a><tt class="py-lineno"> 465</tt>  <tt class="py-line">                <tt class="py-comment">#fda_rule = lstsq(self._fda_mat(1,2).T,matrix([1, 0]).T)[0]</tt> </tt>
<a name="L466"></a><tt class="py-lineno"> 466</tt>  <tt class="py-line">            <tt class="py-keyword">elif</tt> <tt class="py-name">derOrder</tt> <tt class="py-op">==</tt> <tt class="py-number">2</tt><tt class="py-op">:</tt> </tt>
<a name="L467"></a><tt class="py-lineno"> 467</tt>  <tt class="py-line">                <tt class="py-comment"># the even transformation did most of the work, but</tt> </tt>
<a name="L468"></a><tt class="py-lineno"> 468</tt>  <tt class="py-line">                <tt class="py-comment"># we need to kill off the quartic term</tt> </tt>
<a name="L469"></a><tt class="py-lineno"> 469</tt>  <tt class="py-line">                <tt class="py-name">fda_rule</tt> <tt class="py-op">=</tt> <tt class="py-name">matrix</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">pinv</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-14" class="py-name"><a title="numdifftools.core._Derivative._fda_mat" class="py-name" href="#" onclick="return doclink('link-14', '_fda_mat', 'link-11');">_fda_mat</a></tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-number">2</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L470"></a><tt class="py-lineno"> 470</tt>  <tt class="py-line">            <tt class="py-keyword">elif</tt> <tt class="py-name">derOrder</tt> <tt class="py-op">==</tt> <tt class="py-number">3</tt><tt class="py-op">:</tt> </tt>
<a name="L471"></a><tt class="py-lineno"> 471</tt>  <tt class="py-line">                <tt class="py-comment"># the odd transformation did much of the work, but</tt> </tt>
<a name="L472"></a><tt class="py-lineno"> 472</tt>  <tt class="py-line">                <tt class="py-comment"># we need to kill off the linear &amp; quintic terms</tt> </tt>
<a name="L473"></a><tt class="py-lineno"> 473</tt>  <tt class="py-line">                <tt class="py-name">fda_rule</tt> <tt class="py-op">=</tt> <tt class="py-name">matrix</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">pinv</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-15" class="py-name"><a title="numdifftools.core._Derivative._fda_mat" class="py-name" href="#" onclick="return doclink('link-15', '_fda_mat', 'link-11');">_fda_mat</a></tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-number">3</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L474"></a><tt class="py-lineno"> 474</tt>  <tt class="py-line">            <tt class="py-keyword">elif</tt> <tt class="py-name">derOrder</tt> <tt class="py-op">==</tt> <tt class="py-number">4</tt><tt class="py-op">:</tt> </tt>
<a name="L475"></a><tt class="py-lineno"> 475</tt>  <tt class="py-line">                <tt class="py-comment"># the even transformation did much of the work, but</tt> </tt>
<a name="L476"></a><tt class="py-lineno"> 476</tt>  <tt class="py-line">                <tt class="py-comment"># we need to kill off the quadratic and 6th order terms</tt> </tt>
<a name="L477"></a><tt class="py-lineno"> 477</tt>  <tt class="py-line">                <tt class="py-name">fda_rule</tt> <tt class="py-op">=</tt> <tt class="py-name">matrix</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">pinv</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-16" class="py-name"><a title="numdifftools.core._Derivative._fda_mat" class="py-name" href="#" onclick="return doclink('link-16', '_fda_mat', 'link-11');">_fda_mat</a></tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-number">3</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L478"></a><tt class="py-lineno"> 478</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L479"></a><tt class="py-lineno"> 479</tt>  <tt class="py-line">            <tt class="py-comment"># Cases {'forward' 'backward'}</tt> </tt>
<a name="L480"></a><tt class="py-lineno"> 480</tt>  <tt class="py-line">            <tt class="py-comment"># These two cases are identical, except at the very end,</tt> </tt>
<a name="L481"></a><tt class="py-lineno"> 481</tt>  <tt class="py-line">            <tt class="py-comment"># where a sign will be introduced.</tt> </tt>
<a name="L482"></a><tt class="py-lineno"> 482</tt>  <tt class="py-line"> </tt>
<a name="L483"></a><tt class="py-lineno"> 483</tt>  <tt class="py-line">            <tt class="py-comment"># No odd/even trans, but we already dropped</tt> </tt>
<a name="L484"></a><tt class="py-lineno"> 484</tt>  <tt class="py-line">            <tt class="py-comment"># off the constant term</tt> </tt>
<a name="L485"></a><tt class="py-lineno"> 485</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt class="py-name">metOrder</tt> <tt class="py-op">==</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt> </tt>
<a name="L486"></a><tt class="py-lineno"> 486</tt>  <tt class="py-line">                <tt class="py-keyword">if</tt> <tt class="py-name">derOrder</tt> <tt class="py-op">==</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt> </tt>
<a name="L487"></a><tt class="py-lineno"> 487</tt>  <tt class="py-line">                    <tt class="py-comment">#fda_rule[0] = 1</tt> </tt>
<a name="L488"></a><tt class="py-lineno"> 488</tt>  <tt class="py-line">                    <tt class="py-keyword">pass</tt> </tt>
<a name="L489"></a><tt class="py-lineno"> 489</tt>  <tt class="py-line">                <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L490"></a><tt class="py-lineno"> 490</tt>  <tt class="py-line">                    <tt class="py-comment">#% 2:4</tt> </tt>
<a name="L491"></a><tt class="py-lineno"> 491</tt>  <tt class="py-line">                    <tt class="py-name">v</tt> <tt class="py-op">=</tt> <tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-name">derOrder</tt><tt class="py-op">)</tt> </tt>
<a name="L492"></a><tt class="py-lineno"> 492</tt>  <tt class="py-line">                    <tt class="py-name">v</tt><tt class="py-op">[</tt><tt class="py-name">derOrder</tt> <tt class="py-op">-</tt> <tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-number">1</tt> </tt>
<a name="L493"></a><tt class="py-lineno"> 493</tt>  <tt class="py-line">                    <tt class="py-name">fda_rule</tt> <tt class="py-op">=</tt> <tt class="py-name">matrix</tt><tt class="py-op">(</tt><tt class="py-name">v</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">pinv</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-17" class="py-name"><a title="numdifftools.core._Derivative._fda_mat" class="py-name" href="#" onclick="return doclink('link-17', '_fda_mat', 'link-11');">_fda_mat</a></tt><tt class="py-op">(</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-name">derOrder</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L494"></a><tt class="py-lineno"> 494</tt>  <tt class="py-line">            <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L495"></a><tt class="py-lineno"> 495</tt>  <tt class="py-line">                <tt class="py-comment"># par.MethodOrder methods drop off the lower order terms,</tt> </tt>
<a name="L496"></a><tt class="py-lineno"> 496</tt>  <tt class="py-line">                <tt class="py-comment"># plus terms directly above DerivativeOrder</tt> </tt>
<a name="L497"></a><tt class="py-lineno"> 497</tt>  <tt class="py-line">                <tt class="py-name">v</tt> <tt class="py-op">=</tt> <tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-name">derOrder</tt> <tt class="py-op">+</tt> <tt class="py-name">metOrder</tt> <tt class="py-op">-</tt> <tt class="py-number">1</tt><tt class="py-op">)</tt> </tt>
<a name="L498"></a><tt class="py-lineno"> 498</tt>  <tt class="py-line">                <tt class="py-name">v</tt><tt class="py-op">[</tt><tt class="py-name">derOrder</tt> <tt class="py-op">-</tt> <tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-number">1</tt> </tt>
<a name="L499"></a><tt class="py-lineno"> 499</tt>  <tt class="py-line">                <tt class="py-name">dpm</tt> <tt class="py-op">=</tt> <tt class="py-name">derOrder</tt> <tt class="py-op">+</tt> <tt class="py-name">metOrder</tt> <tt class="py-op">-</tt> <tt class="py-number">1</tt> </tt>
<a name="L500"></a><tt class="py-lineno"> 500</tt>  <tt class="py-line">                <tt class="py-name">fda_rule</tt> <tt class="py-op">=</tt> <tt class="py-name">matrix</tt><tt class="py-op">(</tt><tt class="py-name">v</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">pinv</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-18" class="py-name"><a title="numdifftools.core._Derivative._fda_mat" class="py-name" href="#" onclick="return doclink('link-18', '_fda_mat', 'link-11');">_fda_mat</a></tt><tt class="py-op">(</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-name">dpm</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L501"></a><tt class="py-lineno"> 501</tt>  <tt class="py-line">            <tt class="py-comment">#% correct sign for the 'backward' rule</tt> </tt>
<a name="L502"></a><tt class="py-lineno"> 502</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt class="py-name">method</tt> <tt class="py-op">==</tt> <tt class="py-string">'b'</tt><tt class="py-op">:</tt> </tt>
<a name="L503"></a><tt class="py-lineno"> 503</tt>  <tt class="py-line">                <tt class="py-name">fda_rule</tt> <tt class="py-op">=</tt> <tt class="py-op">-</tt><tt class="py-name">fda_rule</tt> </tt>
<a name="L504"></a><tt class="py-lineno"> 504</tt>  <tt class="py-line"> </tt>
<a name="L505"></a><tt class="py-lineno"> 505</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_fda_rule</tt> <tt class="py-op">=</tt> <tt class="py-name">fda_rule</tt><tt class="py-op">.</tt><tt class="py-name">ravel</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
</div><a name="_Derivative._set_delta"></a><div id="_Derivative._set_delta-def"><a name="L506"></a><tt class="py-lineno"> 506</tt> <a class="py-toggle" href="#" id="_Derivative._set_delta-toggle" onclick="return toggle('_Derivative._set_delta');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core._Derivative-class.html#_set_delta">_set_delta</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Derivative._set_delta-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="_Derivative._set_delta-expanded"><a name="L507"></a><tt class="py-lineno"> 507</tt>  <tt class="py-line">        <tt class="py-docstring">''' Set the steps to use in derivation.</tt> </tt>
<a name="L508"></a><tt class="py-lineno"> 508</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L509"></a><tt class="py-lineno"> 509</tt>  <tt class="py-line"><tt class="py-docstring">            Member variables used:</tt> </tt>
<a name="L510"></a><tt class="py-lineno"> 510</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L511"></a><tt class="py-lineno"> 511</tt>  <tt class="py-line"><tt class="py-docstring">            n</tt> </tt>
<a name="L512"></a><tt class="py-lineno"> 512</tt>  <tt class="py-line"><tt class="py-docstring">            order</tt> </tt>
<a name="L513"></a><tt class="py-lineno"> 513</tt>  <tt class="py-line"><tt class="py-docstring">            method</tt> </tt>
<a name="L514"></a><tt class="py-lineno"> 514</tt>  <tt class="py-line"><tt class="py-docstring">            romberg_terms</tt> </tt>
<a name="L515"></a><tt class="py-lineno"> 515</tt>  <tt class="py-line"><tt class="py-docstring">            step_fix</tt> </tt>
<a name="L516"></a><tt class="py-lineno"> 516</tt>  <tt class="py-line"><tt class="py-docstring">            step_max</tt> </tt>
<a name="L517"></a><tt class="py-lineno"> 517</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L518"></a><tt class="py-lineno"> 518</tt>  <tt class="py-line">        <tt class="py-comment"># Always choose the step size h so that</tt> </tt>
<a name="L519"></a><tt class="py-lineno"> 519</tt>  <tt class="py-line">        <tt class="py-comment"># it is an exactly representable number.</tt> </tt>
<a name="L520"></a><tt class="py-lineno"> 520</tt>  <tt class="py-line">        <tt class="py-comment"># This is important when calculating numerical derivatives and is</tt> </tt>
<a name="L521"></a><tt class="py-lineno"> 521</tt>  <tt class="py-line">        <tt class="py-comment">#  accomplished by the following.</tt> </tt>
<a name="L522"></a><tt class="py-lineno"> 522</tt>  <tt class="py-line">        <tt class="py-name">stepRatio</tt> <tt class="py-op">=</tt> <tt class="py-name">float</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">step_ratio</tt> <tt class="py-op">+</tt> <tt class="py-number">1.0</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-number">1.0</tt> </tt>
<a name="L523"></a><tt class="py-lineno"> 523</tt>  <tt class="py-line">         </tt>
<a name="L524"></a><tt class="py-lineno"> 524</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">step_num</tt> <tt class="py-keyword">is</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> </tt>
<a name="L525"></a><tt class="py-lineno"> 525</tt>  <tt class="py-line">            <tt class="py-name">num_steps</tt> <tt class="py-op">=</tt> <tt class="py-number">26</tt> </tt>
<a name="L526"></a><tt class="py-lineno"> 526</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">step_fix</tt><tt class="py-op">:</tt> </tt>
<a name="L527"></a><tt class="py-lineno"> 527</tt>  <tt class="py-line">                <tt class="py-name">num_steps</tt> <tt class="py-op">=</tt> <tt class="py-name">int</tt><tt class="py-op">(</tt><tt class="py-number">3</tt> <tt class="py-op">+</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">ceil</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">n</tt> <tt class="py-op">/</tt> <tt class="py-number">2.</tt><tt class="py-op">)</tt> <tt class="py-op">+</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">order</tt> <tt class="py-op">+</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">romberg_terms</tt> <tt class="py-op">+</tt> <tt class="py-number">4</tt><tt class="py-op">)</tt>  </tt>
<a name="L528"></a><tt class="py-lineno"> 528</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">method</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">==</tt> <tt class="py-string">'c'</tt><tt class="py-op">:</tt> </tt>
<a name="L529"></a><tt class="py-lineno"> 529</tt>  <tt class="py-line">                <tt class="py-name">num_steps</tt> <tt class="py-op">=</tt> <tt class="py-name">num_steps</tt> <tt class="py-op">-</tt> <tt class="py-number">2</tt> </tt>
<a name="L530"></a><tt class="py-lineno"> 530</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L531"></a><tt class="py-lineno"> 531</tt>  <tt class="py-line">            <tt class="py-name">num_steps</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">step_num</tt> </tt>
<a name="L532"></a><tt class="py-lineno"> 532</tt>  <tt class="py-line">             </tt>
<a name="L533"></a><tt class="py-lineno"> 533</tt>  <tt class="py-line">         </tt>
<a name="L534"></a><tt class="py-lineno"> 534</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">step_fix</tt> <tt class="py-keyword">is</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt>       </tt>
<a name="L535"></a><tt class="py-lineno"> 535</tt>  <tt class="py-line">            <tt class="py-name">step1</tt> <tt class="py-op">=</tt> <tt class="py-name">float</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">step_max</tt> <tt class="py-op">+</tt> <tt class="py-number">1.0</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-number">1.0</tt> </tt>
<a name="L536"></a><tt class="py-lineno"> 536</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L537"></a><tt class="py-lineno"> 537</tt>  <tt class="py-line">            <tt class="py-name">step1</tt> <tt class="py-op">=</tt> <tt class="py-name">float</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">step_fix</tt> <tt class="py-op">+</tt> <tt class="py-number">1.0</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-number">1.0</tt> </tt>
<a name="L538"></a><tt class="py-lineno"> 538</tt>  <tt class="py-line">           </tt>
<a name="L539"></a><tt class="py-lineno"> 539</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_delta</tt> <tt class="py-op">=</tt> <tt class="py-name">step1</tt> <tt class="py-op">*</tt> <tt class="py-name">stepRatio</tt> <tt class="py-op">**</tt> <tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">arange</tt><tt class="py-op">(</tt><tt class="py-name">num_steps</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
</div><a name="L540"></a><tt class="py-lineno"> 540</tt>  <tt class="py-line"> </tt>
<a name="L541"></a><tt class="py-lineno"> 541</tt>  <tt class="py-line">        <tt class="py-comment">#hn^N&lt;sqrt(eps)</tt> </tt>
<a name="L542"></a><tt class="py-lineno"> 542</tt>  <tt class="py-line"> </tt>
<a name="_Derivative._set_romb_qr"></a><div id="_Derivative._set_romb_qr-def"><a name="L543"></a><tt class="py-lineno"> 543</tt> <a class="py-toggle" href="#" id="_Derivative._set_romb_qr-toggle" onclick="return toggle('_Derivative._set_romb_qr');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core._Derivative-class.html#_set_romb_qr">_set_romb_qr</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Derivative._set_romb_qr-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="_Derivative._set_romb_qr-expanded"><a name="L544"></a><tt class="py-lineno"> 544</tt>  <tt class="py-line">        <tt class="py-docstring">'''</tt> </tt>
<a name="L545"></a><tt class="py-lineno"> 545</tt>  <tt class="py-line"><tt class="py-docstring">        Member variables used</tt> </tt>
<a name="L546"></a><tt class="py-lineno"> 546</tt>  <tt class="py-line"><tt class="py-docstring">            order</tt> </tt>
<a name="L547"></a><tt class="py-lineno"> 547</tt>  <tt class="py-line"><tt class="py-docstring">            method</tt> </tt>
<a name="L548"></a><tt class="py-lineno"> 548</tt>  <tt class="py-line"><tt class="py-docstring">            romberg_terms</tt> </tt>
<a name="L549"></a><tt class="py-lineno"> 549</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L550"></a><tt class="py-lineno"> 550</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L551"></a><tt class="py-lineno"> 551</tt>  <tt class="py-line">        <tt class="py-name">nexpon</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">romberg_terms</tt> </tt>
<a name="L552"></a><tt class="py-lineno"> 552</tt>  <tt class="py-line">        <tt class="py-name">add1</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">method</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">==</tt> <tt class="py-string">'c'</tt> </tt>
<a name="L553"></a><tt class="py-lineno"> 553</tt>  <tt class="py-line">        <tt class="py-name">rombexpon</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-number">1</tt> <tt class="py-op">+</tt> <tt class="py-name">add1</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">arange</tt><tt class="py-op">(</tt><tt class="py-name">nexpon</tt><tt class="py-op">)</tt> <tt class="py-op">+</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">order</tt> </tt>
<a name="L554"></a><tt class="py-lineno"> 554</tt>  <tt class="py-line">         </tt>
<a name="L555"></a><tt class="py-lineno"> 555</tt>  <tt class="py-line">        <tt class="py-name">srinv</tt> <tt class="py-op">=</tt> <tt class="py-number">1.0</tt> <tt class="py-op">/</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">step_ratio</tt> </tt>
<a name="L556"></a><tt class="py-lineno"> 556</tt>  <tt class="py-line">         </tt>
<a name="L557"></a><tt class="py-lineno"> 557</tt>  <tt class="py-line">        <tt class="py-comment"># do nothing if no romberg terms</tt> </tt>
<a name="L558"></a><tt class="py-lineno"> 558</tt>  <tt class="py-line">        <tt class="py-name">rmat</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">ones</tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">nexpon</tt> <tt class="py-op">+</tt> <tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-name">nexpon</tt> <tt class="py-op">+</tt> <tt class="py-number">1</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L559"></a><tt class="py-lineno"> 559</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">nexpon</tt> <tt class="py-op">&gt;</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L560"></a><tt class="py-lineno"> 560</tt>  <tt class="py-line">            <tt class="py-name">rmat</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">srinv</tt> <tt class="py-op">**</tt> <tt class="py-name">rombexpon</tt> </tt>
<a name="L561"></a><tt class="py-lineno"> 561</tt>  <tt class="py-line">            <tt class="py-keyword">for</tt> <tt class="py-name">n</tt> <tt class="py-keyword">in</tt> <tt class="py-name">range</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-name">nexpon</tt> <tt class="py-op">+</tt> <tt class="py-number">2</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L562"></a><tt class="py-lineno"> 562</tt>  <tt class="py-line">                <tt class="py-name">rmat</tt><tt class="py-op">[</tt><tt class="py-name">n</tt><tt class="py-op">,</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">srinv</tt> <tt class="py-op">**</tt> <tt class="py-op">(</tt><tt class="py-name">n</tt> <tt class="py-op">*</tt> <tt class="py-name">rombexpon</tt><tt class="py-op">)</tt> </tt>
<a name="L563"></a><tt class="py-lineno"> 563</tt>  <tt class="py-line"> </tt>
<a name="L564"></a><tt class="py-lineno"> 564</tt>  <tt class="py-line"> </tt>
<a name="L565"></a><tt class="py-lineno"> 565</tt>  <tt class="py-line">        <tt class="py-name">rmat</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">matrix</tt><tt class="py-op">(</tt><tt class="py-name">rmat</tt><tt class="py-op">)</tt> </tt>
<a name="L566"></a><tt class="py-lineno"> 566</tt>  <tt class="py-line">        <tt class="py-comment"># qr factorization used for the extrapolation as well</tt> </tt>
<a name="L567"></a><tt class="py-lineno"> 567</tt>  <tt class="py-line">        <tt class="py-comment"># as the uncertainty estimates</tt> </tt>
<a name="L568"></a><tt class="py-lineno"> 568</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_qromb</tt><tt class="py-op">,</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_rromb</tt> <tt class="py-op">=</tt> <tt class="py-name">linalg</tt><tt class="py-op">.</tt><tt class="py-name">qr</tt><tt class="py-op">(</tt><tt class="py-name">rmat</tt><tt class="py-op">)</tt> </tt>
<a name="L569"></a><tt class="py-lineno"> 569</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_rmat</tt> <tt class="py-op">=</tt> <tt class="py-name">rmat</tt> </tt>
</div><a name="L570"></a><tt class="py-lineno"> 570</tt>  <tt class="py-line">         </tt>
<a name="L571"></a><tt class="py-lineno"> 571</tt>  <tt class="py-line"> </tt>
<a name="_Derivative._set_difference_function"></a><div id="_Derivative._set_difference_function-def"><a name="L572"></a><tt class="py-lineno"> 572</tt> <a class="py-toggle" href="#" id="_Derivative._set_difference_function-toggle" onclick="return toggle('_Derivative._set_difference_function');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core._Derivative-class.html#_set_difference_function">_set_difference_function</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Derivative._set_difference_function-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="_Derivative._set_difference_function-expanded"><a name="L573"></a><tt class="py-lineno"> 573</tt>  <tt class="py-line">        <tt class="py-docstring">''' Set _fdiff function according to method</tt> </tt>
<a name="L574"></a><tt class="py-lineno"> 574</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L575"></a><tt class="py-lineno"> 575</tt>  <tt class="py-line">        <tt class="py-name">get_diff_fun</tt> <tt class="py-op">=</tt> <tt class="py-name">dict</tt><tt class="py-op">(</tt><tt class="py-name">c</tt><tt class="py-op">=</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-19" class="py-name" targets="Method numdifftools.core._Derivative._central()=numdifftools.core._Derivative-class.html#_central"><a title="numdifftools.core._Derivative._central" class="py-name" href="#" onclick="return doclink('link-19', '_central', 'link-19');">_central</a></tt><tt class="py-op">,</tt> <tt class="py-name">b</tt><tt class="py-op">=</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-20" class="py-name" targets="Method numdifftools.core._Derivative._backward()=numdifftools.core._Derivative-class.html#_backward"><a title="numdifftools.core._Derivative._backward" class="py-name" href="#" onclick="return doclink('link-20', '_backward', 'link-20');">_backward</a></tt><tt class="py-op">,</tt> <tt class="py-name">f</tt><tt class="py-op">=</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-21" class="py-name" targets="Method numdifftools.core._Derivative._forward()=numdifftools.core._Derivative-class.html#_forward"><a title="numdifftools.core._Derivative._forward" class="py-name" href="#" onclick="return doclink('link-21', '_forward', 'link-21');">_forward</a></tt><tt class="py-op">)</tt><tt class="py-op">[</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">method</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">]</tt> </tt>
<a name="L576"></a><tt class="py-lineno"> 576</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_fdiff</tt> <tt class="py-op">=</tt> <tt class="py-name">get_diff_fun</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
</div><a name="L577"></a><tt class="py-lineno"> 577</tt>  <tt class="py-line"> </tt>
<a name="_Derivative._central"></a><div id="_Derivative._central-def"><a name="L578"></a><tt class="py-lineno"> 578</tt> <a class="py-toggle" href="#" id="_Derivative._central-toggle" onclick="return toggle('_Derivative._central');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt>  <a class="py-def-name" href="numdifftools.core._Derivative-class.html#_central">_central</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Derivative._central-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="_Derivative._central-expanded"><a name="L579"></a><tt class="py-lineno"> 579</tt>  <tt class="py-line">        <tt class="py-docstring">''' Return central difference function</tt> </tt>
<a name="L580"></a><tt class="py-lineno"> 580</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L581"></a><tt class="py-lineno"> 581</tt>  <tt class="py-line"><tt class="py-docstring">        Member variables used</tt> </tt>
<a name="L582"></a><tt class="py-lineno"> 582</tt>  <tt class="py-line"><tt class="py-docstring">            n</tt> </tt>
<a name="L583"></a><tt class="py-lineno"> 583</tt>  <tt class="py-line"><tt class="py-docstring">            fun</tt> </tt>
<a name="L584"></a><tt class="py-lineno"> 584</tt>  <tt class="py-line"><tt class="py-docstring">            vectorized</tt> </tt>
<a name="L585"></a><tt class="py-lineno"> 585</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L586"></a><tt class="py-lineno"> 586</tt>  <tt class="py-line">        <tt class="py-comment"># A central rule, so we will need to evaluate</tt> </tt>
<a name="L587"></a><tt class="py-lineno"> 587</tt>  <tt class="py-line">        <tt class="py-comment"># symmetrically around x0i.</tt> </tt>
<a name="L588"></a><tt class="py-lineno"> 588</tt>  <tt class="py-line">        <tt class="py-comment">#fun = self.fun</tt> </tt>
<a name="L589"></a><tt class="py-lineno"> 589</tt>  <tt class="py-line">        <tt class="py-name">evenOrder</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">remainder</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">n</tt><tt class="py-op">,</tt> <tt class="py-number">2</tt><tt class="py-op">)</tt> <tt class="py-op">==</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt>  </tt>
<a name="L590"></a><tt class="py-lineno"> 590</tt>  <tt class="py-line">         </tt>
<a name="L591"></a><tt class="py-lineno"> 591</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">vectorized</tt><tt class="py-op">:</tt> </tt>
<a name="L592"></a><tt class="py-lineno"> 592</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt class="py-name">evenOrder</tt><tt class="py-op">:</tt> </tt>
<a name="L593"></a><tt class="py-lineno"> 593</tt>  <tt class="py-line">                <tt class="py-name">f_del</tt> <tt class="py-op">=</tt> <tt class="py-keyword">lambda</tt> <tt class="py-name">fun</tt><tt class="py-op">,</tt> <tt class="py-name">f_x0i</tt><tt class="py-op">,</tt> <tt class="py-name">x0i</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt><tt class="py-op">:</tt> <tt class="py-op">(</tt><tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">x0i</tt> <tt class="py-op">+</tt> <tt class="py-name">h</tt><tt class="py-op">)</tt> <tt class="py-op">+</tt> <tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">x0i</tt> <tt class="py-op">-</tt> <tt class="py-name">h</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">.</tt><tt class="py-name">ravel</tt><tt class="py-op">(</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-number">2.0</tt> <tt class="py-op">-</tt> <tt class="py-name">f_x0i</tt> </tt>
<a name="L594"></a><tt class="py-lineno"> 594</tt>  <tt class="py-line">            <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L595"></a><tt class="py-lineno"> 595</tt>  <tt class="py-line">                <tt class="py-name">f_del</tt> <tt class="py-op">=</tt> <tt class="py-keyword">lambda</tt> <tt class="py-name">fun</tt><tt class="py-op">,</tt> <tt class="py-name">f_x0i</tt><tt class="py-op">,</tt> <tt class="py-name">x0i</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt><tt class="py-op">:</tt> <tt class="py-op">(</tt><tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">x0i</tt> <tt class="py-op">+</tt> <tt class="py-name">h</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">x0i</tt> <tt class="py-op">-</tt> <tt class="py-name">h</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">.</tt><tt class="py-name">ravel</tt><tt class="py-op">(</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-number">2.0</tt>  </tt>
<a name="L596"></a><tt class="py-lineno"> 596</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L597"></a><tt class="py-lineno"> 597</tt>  <tt class="py-line">            <tt class="py-comment"># not vectorized, so loop</tt> </tt>
<a name="L598"></a><tt class="py-lineno"> 598</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt class="py-name">evenOrder</tt><tt class="py-op">:</tt> </tt>
<a name="L599"></a><tt class="py-lineno"> 599</tt>  <tt class="py-line">                <tt class="py-name">f_del</tt> <tt class="py-op">=</tt> <tt class="py-keyword">lambda</tt> <tt class="py-name">fun</tt><tt class="py-op">,</tt> <tt class="py-name">f_x0i</tt><tt class="py-op">,</tt> <tt class="py-name">x0i</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt><tt class="py-op">:</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">asfarray</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">x0i</tt> <tt class="py-op">+</tt> <tt class="py-name">h_j</tt><tt class="py-op">)</tt> <tt class="py-op">+</tt> <tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">x0i</tt> <tt class="py-op">-</tt> <tt class="py-name">h_j</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt class="py-name">h_j</tt> <tt class="py-keyword">in</tt> <tt class="py-name">h</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">.</tt><tt class="py-name">ravel</tt><tt class="py-op">(</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-number">2.0</tt> <tt class="py-op">-</tt> <tt class="py-name">f_x0i</tt> </tt>
<a name="L600"></a><tt class="py-lineno"> 600</tt>  <tt class="py-line">            <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L601"></a><tt class="py-lineno"> 601</tt>  <tt class="py-line">                <tt class="py-name">f_del</tt> <tt class="py-op">=</tt> <tt class="py-keyword">lambda</tt> <tt class="py-name">fun</tt><tt class="py-op">,</tt> <tt class="py-name">f_x0i</tt><tt class="py-op">,</tt> <tt class="py-name">x0i</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt><tt class="py-op">:</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">asfarray</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">x0i</tt> <tt class="py-op">+</tt> <tt class="py-name">h_j</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">x0i</tt> <tt class="py-op">-</tt> <tt class="py-name">h_j</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt class="py-name">h_j</tt> <tt class="py-keyword">in</tt> <tt class="py-name">h</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">.</tt><tt class="py-name">ravel</tt><tt class="py-op">(</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-number">2.0</tt> </tt>
<a name="L602"></a><tt class="py-lineno"> 602</tt>  <tt class="py-line">            </tt>
<a name="L603"></a><tt class="py-lineno"> 603</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">f_del</tt> </tt>
</div><a name="L604"></a><tt class="py-lineno"> 604</tt>  <tt class="py-line"> </tt>
<a name="_Derivative._forward"></a><div id="_Derivative._forward-def"><a name="L605"></a><tt class="py-lineno"> 605</tt> <a class="py-toggle" href="#" id="_Derivative._forward-toggle" onclick="return toggle('_Derivative._forward');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core._Derivative-class.html#_forward">_forward</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Derivative._forward-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="_Derivative._forward-expanded"><a name="L606"></a><tt class="py-lineno"> 606</tt>  <tt class="py-line">        <tt class="py-docstring">''' Return forward difference function</tt> </tt>
<a name="L607"></a><tt class="py-lineno"> 607</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L608"></a><tt class="py-lineno"> 608</tt>  <tt class="py-line"><tt class="py-docstring">        Member variables used</tt> </tt>
<a name="L609"></a><tt class="py-lineno"> 609</tt>  <tt class="py-line"><tt class="py-docstring">            fun</tt> </tt>
<a name="L610"></a><tt class="py-lineno"> 610</tt>  <tt class="py-line"><tt class="py-docstring">            vectorized</tt> </tt>
<a name="L611"></a><tt class="py-lineno"> 611</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L612"></a><tt class="py-lineno"> 612</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L613"></a><tt class="py-lineno"> 613</tt>  <tt class="py-line">        <tt class="py-comment">#fun = self.fun</tt> </tt>
<a name="L614"></a><tt class="py-lineno"> 614</tt>  <tt class="py-line">        <tt class="py-comment"># drop off the constant only</tt> </tt>
<a name="L615"></a><tt class="py-lineno"> 615</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">vectorized</tt><tt class="py-op">:</tt> </tt>
<a name="L616"></a><tt class="py-lineno"> 616</tt>  <tt class="py-line">            <tt class="py-name">f_del</tt> <tt class="py-op">=</tt> <tt class="py-keyword">lambda</tt> <tt class="py-name">fun</tt><tt class="py-op">,</tt> <tt class="py-name">f_x0i</tt><tt class="py-op">,</tt> <tt class="py-name">x0i</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt><tt class="py-op">:</tt> <tt class="py-op">(</tt><tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">x0i</tt> <tt class="py-op">+</tt> <tt class="py-name">h</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-name">f_x0i</tt><tt class="py-op">)</tt><tt class="py-op">.</tt><tt class="py-name">ravel</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L617"></a><tt class="py-lineno"> 617</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L618"></a><tt class="py-lineno"> 618</tt>  <tt class="py-line">            <tt class="py-name">f_del</tt> <tt class="py-op">=</tt> <tt class="py-keyword">lambda</tt> <tt class="py-name">fun</tt><tt class="py-op">,</tt> <tt class="py-name">f_x0i</tt><tt class="py-op">,</tt> <tt class="py-name">x0i</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt><tt class="py-op">:</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">asfarray</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">x0i</tt> <tt class="py-op">+</tt> <tt class="py-name">h_j</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-name">f_x0i</tt> <tt class="py-keyword">for</tt> <tt class="py-name">h_j</tt> <tt class="py-keyword">in</tt> <tt class="py-name">h</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">.</tt><tt class="py-name">ravel</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L619"></a><tt class="py-lineno"> 619</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">f_del</tt> </tt>
</div><a name="L620"></a><tt class="py-lineno"> 620</tt>  <tt class="py-line"> </tt>
<a name="_Derivative._backward"></a><div id="_Derivative._backward-def"><a name="L621"></a><tt class="py-lineno"> 621</tt> <a class="py-toggle" href="#" id="_Derivative._backward-toggle" onclick="return toggle('_Derivative._backward');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core._Derivative-class.html#_backward">_backward</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Derivative._backward-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="_Derivative._backward-expanded"><a name="L622"></a><tt class="py-lineno"> 622</tt>  <tt class="py-line">        <tt class="py-docstring">''' Return backward difference function</tt> </tt>
<a name="L623"></a><tt class="py-lineno"> 623</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L624"></a><tt class="py-lineno"> 624</tt>  <tt class="py-line"><tt class="py-docstring">        Member variables used</tt> </tt>
<a name="L625"></a><tt class="py-lineno"> 625</tt>  <tt class="py-line"><tt class="py-docstring">        ---------------------</tt> </tt>
<a name="L626"></a><tt class="py-lineno"> 626</tt>  <tt class="py-line"><tt class="py-docstring">        fun</tt> </tt>
<a name="L627"></a><tt class="py-lineno"> 627</tt>  <tt class="py-line"><tt class="py-docstring">        vectorized</tt> </tt>
<a name="L628"></a><tt class="py-lineno"> 628</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L629"></a><tt class="py-lineno"> 629</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L630"></a><tt class="py-lineno"> 630</tt>  <tt class="py-line">        <tt class="py-comment">#fun = self.fun</tt> </tt>
<a name="L631"></a><tt class="py-lineno"> 631</tt>  <tt class="py-line">        <tt class="py-comment">#% drop off the constant only</tt> </tt>
<a name="L632"></a><tt class="py-lineno"> 632</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">vectorized</tt><tt class="py-op">:</tt> </tt>
<a name="L633"></a><tt class="py-lineno"> 633</tt>  <tt class="py-line">            <tt class="py-name">f_del</tt> <tt class="py-op">=</tt> <tt class="py-keyword">lambda</tt> <tt class="py-name">fun</tt><tt class="py-op">,</tt> <tt class="py-name">f_x0i</tt><tt class="py-op">,</tt> <tt class="py-name">x0i</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt><tt class="py-op">:</tt> <tt class="py-op">(</tt><tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">x0i</tt> <tt class="py-op">-</tt> <tt class="py-name">h</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-name">f_x0i</tt><tt class="py-op">)</tt><tt class="py-op">.</tt><tt class="py-name">ravel</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L634"></a><tt class="py-lineno"> 634</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L635"></a><tt class="py-lineno"> 635</tt>  <tt class="py-line">            <tt class="py-name">f_del</tt> <tt class="py-op">=</tt> <tt class="py-keyword">lambda</tt> <tt class="py-name">fun</tt><tt class="py-op">,</tt> <tt class="py-name">f_x0i</tt><tt class="py-op">,</tt> <tt class="py-name">x0i</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt><tt class="py-op">:</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">asfarray</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">x0i</tt> <tt class="py-op">-</tt> <tt class="py-name">h_j</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-name">f_x0i</tt> <tt class="py-keyword">for</tt> <tt class="py-name">h_j</tt> <tt class="py-keyword">in</tt> <tt class="py-name">h</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">.</tt><tt class="py-name">ravel</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L636"></a><tt class="py-lineno"> 636</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">f_del</tt> </tt>
</div><a name="L637"></a><tt class="py-lineno"> 637</tt>  <tt class="py-line"> </tt>
<a name="L638"></a><tt class="py-lineno"> 638</tt>  <tt class="py-line"> </tt>
<a name="L639"></a><tt class="py-lineno"> 639</tt>  <tt class="py-line"> </tt>
<a name="_Derivative._romb_extrap"></a><div id="_Derivative._romb_extrap-def"><a name="L640"></a><tt class="py-lineno"> 640</tt> <a class="py-toggle" href="#" id="_Derivative._romb_extrap-toggle" onclick="return toggle('_Derivative._romb_extrap');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core._Derivative-class.html#_romb_extrap">_romb_extrap</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">der_init</tt><tt class="py-op">,</tt> <tt class="py-param">h1</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Derivative._romb_extrap-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="_Derivative._romb_extrap-expanded"><a name="L641"></a><tt class="py-lineno"> 641</tt>  <tt class="py-line">        <tt class="py-docstring">''' Return Romberg extrapolated derivatives and error estimates</tt> </tt>
<a name="L642"></a><tt class="py-lineno"> 642</tt>  <tt class="py-line"><tt class="py-docstring">            based on the initial derivative estimates</tt> </tt>
<a name="L643"></a><tt class="py-lineno"> 643</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L644"></a><tt class="py-lineno"> 644</tt>  <tt class="py-line"><tt class="py-docstring">        Parameter</tt> </tt>
<a name="L645"></a><tt class="py-lineno"> 645</tt>  <tt class="py-line"><tt class="py-docstring">        ---------</tt> </tt>
<a name="L646"></a><tt class="py-lineno"> 646</tt>  <tt class="py-line"><tt class="py-docstring">        der_init - initial derivative estimates</tt> </tt>
<a name="L647"></a><tt class="py-lineno"> 647</tt>  <tt class="py-line"><tt class="py-docstring">        h1 - stepsizes used in the derivative estimates</tt> </tt>
<a name="L648"></a><tt class="py-lineno"> 648</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L649"></a><tt class="py-lineno"> 649</tt>  <tt class="py-line"><tt class="py-docstring">        Returns</tt> </tt>
<a name="L650"></a><tt class="py-lineno"> 650</tt>  <tt class="py-line"><tt class="py-docstring">        -------</tt> </tt>
<a name="L651"></a><tt class="py-lineno"> 651</tt>  <tt class="py-line"><tt class="py-docstring">        der_romb - derivative estimates returned</tt> </tt>
<a name="L652"></a><tt class="py-lineno"> 652</tt>  <tt class="py-line"><tt class="py-docstring">        errest - error estimates</tt> </tt>
<a name="L653"></a><tt class="py-lineno"> 653</tt>  <tt class="py-line"><tt class="py-docstring">        hout - stepsizes returned</tt> </tt>
<a name="L654"></a><tt class="py-lineno"> 654</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L655"></a><tt class="py-lineno"> 655</tt>  <tt class="py-line"><tt class="py-docstring">        Member variables used</tt> </tt>
<a name="L656"></a><tt class="py-lineno"> 656</tt>  <tt class="py-line"><tt class="py-docstring">        ---------------------</tt> </tt>
<a name="L657"></a><tt class="py-lineno"> 657</tt>  <tt class="py-line"><tt class="py-docstring">        step_ratio - Ratio decrease in step</tt> </tt>
<a name="L658"></a><tt class="py-lineno"> 658</tt>  <tt class="py-line"><tt class="py-docstring">        rombexpon - higher order terms to cancel using the romberg step</tt> </tt>
<a name="L659"></a><tt class="py-lineno"> 659</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L660"></a><tt class="py-lineno"> 660</tt>  <tt class="py-line">        </tt>
<a name="L661"></a><tt class="py-lineno"> 661</tt>  <tt class="py-line"> </tt>
<a name="L662"></a><tt class="py-lineno"> 662</tt>  <tt class="py-line">        <tt class="py-comment"># amp - noise amplification factor due to the romberg step</tt> </tt>
<a name="L663"></a><tt class="py-lineno"> 663</tt>  <tt class="py-line">        <tt class="py-comment"># the noise amplification is further amplified by the Romberg step.</tt> </tt>
<a name="L664"></a><tt class="py-lineno"> 664</tt>  <tt class="py-line">        <tt class="py-comment"># amp = cond(rromb)</tt> </tt>
<a name="L665"></a><tt class="py-lineno"> 665</tt>  <tt class="py-line"> </tt>
<a name="L666"></a><tt class="py-lineno"> 666</tt>  <tt class="py-line">        <tt class="py-name">isnonfinite</tt> <tt class="py-op">=</tt> <tt class="py-number">1</tt> <tt class="py-op">-</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">isfinite</tt><tt class="py-op">(</tt><tt class="py-name">der_init</tt><tt class="py-op">)</tt> </tt>
<a name="L667"></a><tt class="py-lineno"> 667</tt>  <tt class="py-line">        <tt class="py-name">i_nonfinite</tt><tt class="py-op">,</tt> <tt class="py-op">=</tt> <tt class="py-name">isnonfinite</tt><tt class="py-op">.</tt><tt class="py-name">ravel</tt><tt class="py-op">(</tt><tt class="py-op">)</tt><tt class="py-op">.</tt><tt class="py-name">nonzero</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L668"></a><tt class="py-lineno"> 668</tt>  <tt class="py-line">        <tt class="py-name">hout</tt> <tt class="py-op">=</tt> <tt class="py-name">h1</tt> </tt>
<a name="L669"></a><tt class="py-lineno"> 669</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">i_nonfinite</tt><tt class="py-op">.</tt><tt class="py-name">size</tt> <tt class="py-op">&gt;</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L670"></a><tt class="py-lineno"> 670</tt>  <tt class="py-line">            <tt class="py-name">allfinite_start</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">max</tt><tt class="py-op">(</tt><tt class="py-name">i_nonfinite</tt><tt class="py-op">)</tt> <tt class="py-op">+</tt> <tt class="py-number">1</tt> </tt>
<a name="L671"></a><tt class="py-lineno"> 671</tt>  <tt class="py-line">            <tt class="py-name">der_init</tt> <tt class="py-op">=</tt> <tt class="py-name">der_init</tt><tt class="py-op">[</tt><tt class="py-name">allfinite_start</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> </tt>
<a name="L672"></a><tt class="py-lineno"> 672</tt>  <tt class="py-line">            <tt class="py-name">hout</tt> <tt class="py-op">=</tt> <tt class="py-name">h1</tt><tt class="py-op">[</tt><tt class="py-name">allfinite_start</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> </tt>
<a name="L673"></a><tt class="py-lineno"> 673</tt>  <tt class="py-line">        <tt class="py-comment"># this does the extrapolation to a zero step size.</tt> </tt>
<a name="L674"></a><tt class="py-lineno"> 674</tt>  <tt class="py-line">        <tt class="py-name">nexpon</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">romberg_terms</tt> <tt class="py-comment">#self._nexpon</tt> </tt>
<a name="L675"></a><tt class="py-lineno"> 675</tt>  <tt class="py-line">        <tt class="py-name">ne</tt> <tt class="py-op">=</tt> <tt class="py-name">der_init</tt><tt class="py-op">.</tt><tt class="py-name">size</tt> </tt>
<a name="L676"></a><tt class="py-lineno"> 676</tt>  <tt class="py-line">        <tt class="py-name">rhs</tt> <tt class="py-op">=</tt> <tt id="link-22" class="py-name"><a title="numdifftools.core.vec2mat" class="py-name" href="#" onclick="return doclink('link-22', 'vec2mat', 'link-7');">vec2mat</a></tt><tt class="py-op">(</tt><tt class="py-name">der_init</tt><tt class="py-op">,</tt> <tt class="py-name">nexpon</tt> <tt class="py-op">+</tt> <tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-name">max</tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-name">ne</tt> <tt class="py-op">-</tt> <tt class="py-op">(</tt><tt class="py-name">nexpon</tt> <tt class="py-op">+</tt> <tt class="py-number">2</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L677"></a><tt class="py-lineno"> 677</tt>  <tt class="py-line"> </tt>
<a name="L678"></a><tt class="py-lineno"> 678</tt>  <tt class="py-line">        <tt class="py-name">rombcoefs</tt> <tt class="py-op">=</tt> <tt class="py-name">linalg</tt><tt class="py-op">.</tt><tt class="py-name">lstsq</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_rromb</tt><tt class="py-op">,</tt> <tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_qromb</tt><tt class="py-op">.</tt><tt class="py-name">T</tt> <tt class="py-op">*</tt> <tt class="py-name">rhs</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L679"></a><tt class="py-lineno"> 679</tt>  <tt class="py-line">        <tt class="py-name">der_romb</tt> <tt class="py-op">=</tt> <tt class="py-name">rombcoefs</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-op">:</tt><tt class="py-op">]</tt> </tt>
<a name="L680"></a><tt class="py-lineno"> 680</tt>  <tt class="py-line">         </tt>
<a name="L681"></a><tt class="py-lineno"> 681</tt>  <tt class="py-line">        <tt class="py-name">hout</tt> <tt class="py-op">=</tt> <tt class="py-name">hout</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-name">der_romb</tt><tt class="py-op">.</tt><tt class="py-name">size</tt><tt class="py-op">]</tt> </tt>
<a name="L682"></a><tt class="py-lineno"> 682</tt>  <tt class="py-line">        <tt class="py-name">sqrt</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">sqrt</tt> </tt>
<a name="L683"></a><tt class="py-lineno"> 683</tt>  <tt class="py-line">        <tt class="py-name">sum</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">sum</tt> <tt class="py-comment">#@ReservedAssignment</tt> </tt>
<a name="L684"></a><tt class="py-lineno"> 684</tt>  <tt class="py-line">        <tt class="py-name">asarray</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">asarray</tt> </tt>
<a name="L685"></a><tt class="py-lineno"> 685</tt>  <tt class="py-line">        <tt class="py-comment"># uncertainty estimate of derivative prediction</tt> </tt>
<a name="L686"></a><tt class="py-lineno"> 686</tt>  <tt class="py-line">        <tt class="py-name">s</tt> <tt class="py-op">=</tt> <tt class="py-name">sqrt</tt><tt class="py-op">(</tt><tt class="py-name">sum</tt><tt class="py-op">(</tt><tt class="py-name">asarray</tt><tt class="py-op">(</tt><tt class="py-name">rhs</tt> <tt class="py-op">-</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_rmat</tt> <tt class="py-op">*</tt> <tt class="py-name">rombcoefs</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> <tt class="py-op">**</tt> <tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-name">axis</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L687"></a><tt class="py-lineno"> 687</tt>  <tt class="py-line">        <tt class="py-name">rinv</tt> <tt class="py-op">=</tt> <tt class="py-name">asarray</tt><tt class="py-op">(</tt><tt class="py-name">linalg</tt><tt class="py-op">.</tt><tt class="py-name">pinv</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_rromb</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L688"></a><tt class="py-lineno"> 688</tt>  <tt class="py-line">        <tt class="py-name">cov1</tt> <tt class="py-op">=</tt> <tt class="py-name">sum</tt><tt class="py-op">(</tt><tt class="py-name">rinv</tt> <tt class="py-op">**</tt> <tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-name">axis</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">)</tt> <tt class="py-comment"># 1 spare dof</tt> </tt>
<a name="L689"></a><tt class="py-lineno"> 689</tt>  <tt class="py-line">        <tt class="py-name">eps</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">finfo</tt><tt class="py-op">(</tt><tt class="py-name">float</tt><tt class="py-op">)</tt><tt class="py-op">.</tt><tt class="py-name">eps</tt> </tt>
<a name="L690"></a><tt class="py-lineno"> 690</tt>  <tt class="py-line">        <tt class="py-name">errest</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">maximum</tt><tt class="py-op">(</tt><tt class="py-name">s</tt> <tt class="py-op">*</tt> <tt class="py-number">12.7062047361747</tt> <tt class="py-op">*</tt> <tt class="py-name">sqrt</tt><tt class="py-op">(</tt><tt class="py-name">cov1</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">s</tt> <tt class="py-op">*</tt> <tt class="py-name">eps</tt> <tt class="py-op">*</tt> <tt class="py-number">10.</tt><tt class="py-op">)</tt> </tt>
<a name="L691"></a><tt class="py-lineno"> 691</tt>  <tt class="py-line">        <tt class="py-name">errest</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">where</tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">==</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-name">eps</tt><tt class="py-op">,</tt> <tt class="py-name">errest</tt><tt class="py-op">)</tt> </tt>
<a name="L692"></a><tt class="py-lineno"> 692</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">der_romb</tt><tt class="py-op">.</tt><tt class="py-name">size</tt> <tt class="py-op">&gt;</tt> <tt class="py-number">2</tt><tt class="py-op">:</tt> </tt>
<a name="L693"></a><tt class="py-lineno"> 693</tt>  <tt class="py-line">            <tt class="py-name">der_romb</tt><tt class="py-op">,</tt> <tt class="py-name">err_dea</tt> <tt class="py-op">=</tt> <tt id="link-23" class="py-name" targets="Function numdifftools.core.dea3()=numdifftools.core-module.html#dea3"><a title="numdifftools.core.dea3" class="py-name" href="#" onclick="return doclink('link-23', 'dea3', 'link-23');">dea3</a></tt><tt class="py-op">(</tt><tt class="py-name">der_romb</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">2</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">der_romb</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> </tt>
<a name="L694"></a><tt class="py-lineno"> 694</tt>  <tt class="py-line">                                        <tt class="py-name">der_romb</tt><tt class="py-op">[</tt><tt class="py-number">2</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L695"></a><tt class="py-lineno"> 695</tt>  <tt class="py-line">            <tt class="py-name">errest</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">maximum</tt><tt class="py-op">(</tt><tt class="py-name">errest</tt><tt class="py-op">[</tt><tt class="py-number">2</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">err_dea</tt><tt class="py-op">)</tt> </tt>
<a name="L696"></a><tt class="py-lineno"> 696</tt>  <tt class="py-line">            <tt class="py-name">hout</tt> <tt class="py-op">=</tt> <tt class="py-name">hout</tt><tt class="py-op">[</tt><tt class="py-number">2</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> </tt>
<a name="L697"></a><tt class="py-lineno"> 697</tt>  <tt class="py-line">        <tt class="py-comment">#der_dea, err_dea = dea3(der_init[0:-2],der_init[1:-1],der_init[2:])</tt> </tt>
<a name="L698"></a><tt class="py-lineno"> 698</tt>  <tt class="py-line"> </tt>
<a name="L699"></a><tt class="py-lineno"> 699</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">der_romb</tt><tt class="py-op">,</tt> <tt class="py-name">errest</tt><tt class="py-op">,</tt> <tt class="py-name">hout</tt> </tt>
</div></div><a name="L700"></a><tt class="py-lineno"> 700</tt>  <tt class="py-line">        <tt class="py-comment">#end % _romb_extrap</tt> </tt>
<a name="L701"></a><tt class="py-lineno"> 701</tt>  <tt class="py-line"> </tt>
<a name="_PartialDerivative"></a><div id="_PartialDerivative-def"><a name="L702"></a><tt class="py-lineno"> 702</tt> <a class="py-toggle" href="#" id="_PartialDerivative-toggle" onclick="return toggle('_PartialDerivative');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="numdifftools.core._PartialDerivative-class.html">_PartialDerivative</a><tt class="py-op">(</tt><tt class="py-base-class">_Derivative</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_PartialDerivative-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="_PartialDerivative-expanded"><a name="_PartialDerivative._partial_der"></a><div id="_PartialDerivative._partial_der-def"><a name="L703"></a><tt class="py-lineno"> 703</tt> <a class="py-toggle" href="#" id="_PartialDerivative._partial_der-toggle" onclick="return toggle('_PartialDerivative._partial_der');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core._PartialDerivative-class.html#_partial_der">_partial_der</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x00</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_PartialDerivative._partial_der-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="_PartialDerivative._partial_der-expanded"><a name="L704"></a><tt class="py-lineno"> 704</tt>  <tt class="py-line">        <tt class="py-docstring">''' Return partial derivatives</tt> </tt>
<a name="L705"></a><tt class="py-lineno"> 705</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L706"></a><tt class="py-lineno"> 706</tt>  <tt class="py-line">        <tt class="py-name">x0</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">atleast_1d</tt><tt class="py-op">(</tt><tt class="py-name">x00</tt><tt class="py-op">)</tt> </tt>
<a name="L707"></a><tt class="py-lineno"> 707</tt>  <tt class="py-line">        <tt class="py-name">nx</tt> <tt class="py-op">=</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">)</tt> </tt>
<a name="L708"></a><tt class="py-lineno"> 708</tt>  <tt class="py-line"> </tt>
<a name="L709"></a><tt class="py-lineno"> 709</tt>  <tt class="py-line">        <tt class="py-name">PD</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-name">nx</tt><tt class="py-op">)</tt> </tt>
<a name="L710"></a><tt class="py-lineno"> 710</tt>  <tt class="py-line">        <tt class="py-name">err</tt> <tt class="py-op">=</tt> <tt class="py-name">PD</tt><tt class="py-op">.</tt><tt class="py-name">copy</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L711"></a><tt class="py-lineno"> 711</tt>  <tt class="py-line">        <tt class="py-name">finaldelta</tt> <tt class="py-op">=</tt> <tt class="py-name">PD</tt><tt class="py-op">.</tt><tt class="py-name">copy</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L712"></a><tt class="py-lineno"> 712</tt>  <tt class="py-line">         </tt>
<a name="L713"></a><tt class="py-lineno"> 713</tt>  <tt class="py-line">        <tt class="py-name">stepNom</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-name">None</tt><tt class="py-op">,</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-name">nx</tt> <tt class="py-keyword">if</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">step_nom</tt> <tt class="py-keyword">is</tt> <tt class="py-name">None</tt> <tt class="py-keyword">else</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">step_nom</tt>  </tt>
<a name="L714"></a><tt class="py-lineno"> 714</tt>  <tt class="py-line">         </tt>
<a name="L715"></a><tt class="py-lineno"> 715</tt>  <tt class="py-line">        <tt class="py-name">fun</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-24" class="py-name" targets="Method numdifftools.core._PartialDerivative._fun()=numdifftools.core._PartialDerivative-class.html#_fun"><a title="numdifftools.core._PartialDerivative._fun" class="py-name" href="#" onclick="return doclink('link-24', '_fun', 'link-24');">_fun</a></tt> </tt>
<a name="L716"></a><tt class="py-lineno"> 716</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_x</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">asarray</tt><tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">,</tt> <tt class="py-name">dtype</tt><tt class="py-op">=</tt><tt class="py-name">float</tt><tt class="py-op">)</tt> </tt>
<a name="L717"></a><tt class="py-lineno"> 717</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-name">ind</tt> <tt class="py-keyword">in</tt> <tt class="py-name">range</tt><tt class="py-op">(</tt><tt class="py-name">nx</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L718"></a><tt class="py-lineno"> 718</tt>  <tt class="py-line">            <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_ix</tt> <tt class="py-op">=</tt> <tt class="py-name">ind</tt> </tt>
<a name="L719"></a><tt class="py-lineno"> 719</tt>  <tt class="py-line">            <tt class="py-name">PD</tt><tt class="py-op">[</tt><tt class="py-name">ind</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-25" class="py-name" targets="Method numdifftools.core._Derivative._derivative()=numdifftools.core._Derivative-class.html#_derivative,Method numdifftools.nd_algopy._Common._derivative()=numdifftools.nd_algopy._Common-class.html#_derivative,Method numdifftools.nd_scientific._Common._derivative()=numdifftools.nd_scientific._Common-class.html#_derivative"><a title="numdifftools.core._Derivative._derivative
numdifftools.nd_algopy._Common._derivative
numdifftools.nd_scientific._Common._derivative" class="py-name" href="#" onclick="return doclink('link-25', '_derivative', 'link-25');">_derivative</a></tt><tt class="py-op">(</tt><tt class="py-name">fun</tt><tt class="py-op">,</tt> <tt class="py-name">x0</tt><tt class="py-op">[</tt><tt class="py-name">ind</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">stepNom</tt><tt class="py-op">[</tt><tt class="py-name">ind</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L720"></a><tt class="py-lineno"> 720</tt>  <tt class="py-line">            <tt class="py-name">err</tt><tt class="py-op">[</tt><tt class="py-name">ind</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">error_estimate</tt> </tt>
<a name="L721"></a><tt class="py-lineno"> 721</tt>  <tt class="py-line">            <tt class="py-name">finaldelta</tt><tt class="py-op">[</tt><tt class="py-name">ind</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">finaldelta</tt> </tt>
<a name="L722"></a><tt class="py-lineno"> 722</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">error_estimate</tt> <tt class="py-op">=</tt> <tt class="py-name">err</tt> </tt>
<a name="L723"></a><tt class="py-lineno"> 723</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">finaldelta</tt> <tt class="py-op">=</tt> <tt class="py-name">finaldelta</tt> </tt>
<a name="L724"></a><tt class="py-lineno"> 724</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">PD</tt> </tt>
</div><a name="L725"></a><tt class="py-lineno"> 725</tt>  <tt class="py-line"> </tt>
<a name="_PartialDerivative._fun"></a><div id="_PartialDerivative._fun-def"><a name="L726"></a><tt class="py-lineno"> 726</tt> <a class="py-toggle" href="#" id="_PartialDerivative._fun-toggle" onclick="return toggle('_PartialDerivative._fun');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core._PartialDerivative-class.html#_fun">_fun</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">xi</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_PartialDerivative._fun-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="_PartialDerivative._fun-expanded"><a name="L727"></a><tt class="py-lineno"> 727</tt>  <tt class="py-line">        <tt class="py-name">x</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_x</tt><tt class="py-op">.</tt><tt class="py-name">copy</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L728"></a><tt class="py-lineno"> 728</tt>  <tt class="py-line">        <tt class="py-name">x</tt><tt class="py-op">[</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_ix</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">xi</tt> </tt>
<a name="L729"></a><tt class="py-lineno"> 729</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt>  <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">x</tt><tt class="py-op">)</tt> </tt>
</div></div><a name="L730"></a><tt class="py-lineno"> 730</tt>  <tt class="py-line"> </tt>
<a name="L731"></a><tt class="py-lineno"> 731</tt>  <tt class="py-line"> </tt>
<a name="L732"></a><tt class="py-lineno"> 732</tt>  <tt class="py-line">     </tt>
<a name="L733"></a><tt class="py-lineno"> 733</tt>  <tt class="py-line"><tt class="py-comment">##'''</tt> </tt>
<a name="L734"></a><tt class="py-lineno"> 734</tt>  <tt class="py-line"><tt class="py-comment">##     Arguments: (output)</tt> </tt>
<a name="L735"></a><tt class="py-lineno"> 735</tt>  <tt class="py-line"><tt class="py-comment">##      der     = derivative estimate for each element of x0</tt> </tt>
<a name="L736"></a><tt class="py-lineno"> 736</tt>  <tt class="py-line"><tt class="py-comment">##      errest  = 95% uncertainty estimate of the derivative, such that</tt> </tt>
<a name="L737"></a><tt class="py-lineno"> 737</tt>  <tt class="py-line"><tt class="py-comment">##                 abs(der(j) - f'(x0(j))) &lt; erest(j)</tt> </tt>
<a name="L738"></a><tt class="py-lineno"> 738</tt>  <tt class="py-line"><tt class="py-comment">##        fstep = The final overall stepsize chosen by DERIVEST</tt> </tt>
<a name="L739"></a><tt class="py-lineno"> 739</tt>  <tt class="py-line"><tt class="py-comment">##</tt> </tt>
<a name="L740"></a><tt class="py-lineno"> 740</tt>  <tt class="py-line"><tt class="py-comment">##     Arguments (input)</tt> </tt>
<a name="L741"></a><tt class="py-lineno"> 741</tt>  <tt class="py-line"><tt class="py-comment">##      fun = function to differentiate.</tt> </tt>
<a name="L742"></a><tt class="py-lineno"> 742</tt>  <tt class="py-line"><tt class="py-comment">##            IF fun is not vectorized, you MUST set 'vectorized' to False.</tt> </tt>
<a name="L743"></a><tt class="py-lineno"> 743</tt>  <tt class="py-line"><tt class="py-comment">##      x0  = scalar, vector, or array of points at which to differentiate fun.</tt> </tt>
<a name="L744"></a><tt class="py-lineno"> 744</tt>  <tt class="py-line"><tt class="py-comment">##</tt> </tt>
<a name="L745"></a><tt class="py-lineno"> 745</tt>  <tt class="py-line"><tt class="py-comment">##    '''</tt> </tt>
<a name="Derivative"></a><div id="Derivative-def"><a name="L746"></a><tt class="py-lineno"> 746</tt> <a class="py-toggle" href="#" id="Derivative-toggle" onclick="return toggle('Derivative');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="numdifftools.core.Derivative-class.html">Derivative</a><tt class="py-op">(</tt><tt class="py-base-class">_Derivative</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Derivative-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="Derivative-expanded"><a name="L747"></a><tt class="py-lineno"> 747</tt>  <tt class="py-line">    <tt id="link-26" class="py-name" targets="Variable numdifftools.core.Derivative.__doc__=numdifftools.core.Derivative-class.html#__doc__,Variable numdifftools.core.Gradient.__doc__=numdifftools.core.Gradient-class.html#__doc__,Variable numdifftools.core.Hessdiag.__doc__=numdifftools.core.Hessdiag-class.html#__doc__,Variable numdifftools.core.Hessian.__doc__=numdifftools.core.Hessian-class.html#__doc__,Variable numdifftools.core.Jacobian.__doc__=numdifftools.core.Jacobian-class.html#__doc__"><a title="numdifftools.core.Derivative.__doc__
numdifftools.core.Gradient.__doc__
numdifftools.core.Hessdiag.__doc__
numdifftools.core.Hessian.__doc__
numdifftools.core.Jacobian.__doc__" class="py-name" href="#" onclick="return doclink('link-26', '__doc__', 'link-26');">__doc__</a></tt> <tt class="py-op">=</tt>  <tt class="py-op">(</tt> <tt class="py-comment">#@ReservedAssignment</tt> </tt>
<a name="L748"></a><tt class="py-lineno"> 748</tt>  <tt class="py-line"><tt class="py-string">'''Estimate n'th derivative of fun at x0, with error estimate </tt> </tt>
<a name="L749"></a><tt class="py-lineno"> 749</tt>  <tt class="py-line"><tt class="py-string">    '''</tt> <tt class="py-op">+</tt> <tt id="link-27" class="py-name" targets="Class numdifftools.core._Derivative=numdifftools.core._Derivative-class.html"><a title="numdifftools.core._Derivative" class="py-name" href="#" onclick="return doclink('link-27', '_Derivative', 'link-27');">_Derivative</a></tt><tt class="py-op">.</tt><tt id="link-28" class="py-name"><a title="numdifftools.core.Derivative.__doc__
numdifftools.core.Gradient.__doc__
numdifftools.core.Hessdiag.__doc__
numdifftools.core.Hessian.__doc__
numdifftools.core.Jacobian.__doc__" class="py-name" href="#" onclick="return doclink('link-28', '__doc__', 'link-26');">__doc__</a></tt><tt class="py-op">.</tt><tt class="py-name">partition</tt><tt class="py-op">(</tt><tt class="py-string">'\n'</tt><tt class="py-op">)</tt><tt class="py-op">[</tt><tt class="py-number">2</tt><tt class="py-op">]</tt> <tt class="py-op">+</tt> <tt class="py-string">'''</tt> </tt>
<a name="L750"></a><tt class="py-lineno"> 750</tt>  <tt class="py-line"><tt class="py-string">    Examples</tt> </tt>
<a name="L751"></a><tt class="py-lineno"> 751</tt>  <tt class="py-line"><tt class="py-string">    --------</tt> </tt>
<a name="L752"></a><tt class="py-lineno"> 752</tt>  <tt class="py-line"><tt class="py-string">     &gt;&gt;&gt; import numpy as np</tt> </tt>
<a name="L753"></a><tt class="py-lineno"> 753</tt>  <tt class="py-line"><tt class="py-string">     &gt;&gt;&gt; import numdifftools as nd</tt> </tt>
<a name="L754"></a><tt class="py-lineno"> 754</tt>  <tt class="py-line"><tt class="py-string">     </tt> </tt>
<a name="L755"></a><tt class="py-lineno"> 755</tt>  <tt class="py-line"><tt class="py-string">     # 1'st and 2'nd derivative of exp(x), at x == 1</tt> </tt>
<a name="L756"></a><tt class="py-lineno"> 756</tt>  <tt class="py-line"><tt class="py-string">     &gt;&gt;&gt; fd = nd.Derivative(np.exp)              # 1'st derivative</tt> </tt>
<a name="L757"></a><tt class="py-lineno"> 757</tt>  <tt class="py-line"><tt class="py-string">     &gt;&gt;&gt; fdd = nd.Derivative(np.exp,n=2)  # 2'nd derivative</tt> </tt>
<a name="L758"></a><tt class="py-lineno"> 758</tt>  <tt class="py-line"><tt class="py-string">     &gt;&gt;&gt; fd(1)</tt> </tt>
<a name="L759"></a><tt class="py-lineno"> 759</tt>  <tt class="py-line"><tt class="py-string">     array([ 2.71828183])</tt> </tt>
<a name="L760"></a><tt class="py-lineno"> 760</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L761"></a><tt class="py-lineno"> 761</tt>  <tt class="py-line"><tt class="py-string">     &gt;&gt;&gt; d2 = fdd([1, 2])</tt> </tt>
<a name="L762"></a><tt class="py-lineno"> 762</tt>  <tt class="py-line"><tt class="py-string">     &gt;&gt;&gt; d2</tt> </tt>
<a name="L763"></a><tt class="py-lineno"> 763</tt>  <tt class="py-line"><tt class="py-string">     array([ 2.71828183,  7.3890561 ])</tt> </tt>
<a name="L764"></a><tt class="py-lineno"> 764</tt>  <tt class="py-line"><tt class="py-string">     </tt> </tt>
<a name="L765"></a><tt class="py-lineno"> 765</tt>  <tt class="py-line"><tt class="py-string">     &gt;&gt;&gt; np.abs(d2-np.exp([1,2]))&lt; fdd.error_estimate # Check error estimate</tt> </tt>
<a name="L766"></a><tt class="py-lineno"> 766</tt>  <tt class="py-line"><tt class="py-string">     array([ True,  True], dtype=bool)</tt> </tt>
<a name="L767"></a><tt class="py-lineno"> 767</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L768"></a><tt class="py-lineno"> 768</tt>  <tt class="py-line"><tt class="py-string">     # 3'rd derivative of x.^3+x.^4, at x = [0,1]</tt> </tt>
<a name="L769"></a><tt class="py-lineno"> 769</tt>  <tt class="py-line"><tt class="py-string">     &gt;&gt;&gt; fun = lambda x: x**3 + x**4</tt> </tt>
<a name="L770"></a><tt class="py-lineno"> 770</tt>  <tt class="py-line"><tt class="py-string">     &gt;&gt;&gt; dfun = lambda x: 6 + 4*3*2*np.asarray(x)</tt> </tt>
<a name="L771"></a><tt class="py-lineno"> 771</tt>  <tt class="py-line"><tt class="py-string">     &gt;&gt;&gt; fd3 = nd.Derivative(fun,n=3)</tt> </tt>
<a name="L772"></a><tt class="py-lineno"> 772</tt>  <tt class="py-line"><tt class="py-string">     &gt;&gt;&gt; fd3([0,1])          #  True derivatives: [6,30]</tt> </tt>
<a name="L773"></a><tt class="py-lineno"> 773</tt>  <tt class="py-line"><tt class="py-string">     array([  6.,  30.])</tt> </tt>
<a name="L774"></a><tt class="py-lineno"> 774</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L775"></a><tt class="py-lineno"> 775</tt>  <tt class="py-line"><tt class="py-string">     &gt;&gt;&gt; np.abs(fd3([0,1])-dfun([0,1])) &lt;= fd3.error_estimate</tt> </tt>
<a name="L776"></a><tt class="py-lineno"> 776</tt>  <tt class="py-line"><tt class="py-string">     array([ True,  True], dtype=bool)</tt> </tt>
<a name="L777"></a><tt class="py-lineno"> 777</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L778"></a><tt class="py-lineno"> 778</tt>  <tt class="py-line"><tt class="py-string">     See also</tt> </tt>
<a name="L779"></a><tt class="py-lineno"> 779</tt>  <tt class="py-line"><tt class="py-string">     --------</tt> </tt>
<a name="L780"></a><tt class="py-lineno"> 780</tt>  <tt class="py-line"><tt class="py-string">     Gradient,</tt> </tt>
<a name="L781"></a><tt class="py-lineno"> 781</tt>  <tt class="py-line"><tt class="py-string">     Hessdiag,</tt> </tt>
<a name="L782"></a><tt class="py-lineno"> 782</tt>  <tt class="py-line"><tt class="py-string">     Hessian,</tt> </tt>
<a name="L783"></a><tt class="py-lineno"> 783</tt>  <tt class="py-line"><tt class="py-string">     Jacobian</tt> </tt>
<a name="L784"></a><tt class="py-lineno"> 784</tt>  <tt class="py-line"><tt class="py-string">    '''</tt><tt class="py-op">)</tt> </tt>
<a name="L785"></a><tt class="py-lineno"> 785</tt>  <tt class="py-line"> </tt>
<a name="Derivative.__call__"></a><div id="Derivative.__call__-def"><a name="L786"></a><tt class="py-lineno"> 786</tt> <a class="py-toggle" href="#" id="Derivative.__call__-toggle" onclick="return toggle('Derivative.__call__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core.Derivative-class.html#__call__">__call__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x00</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Derivative.__call__-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="Derivative.__call__-expanded"><a name="L787"></a><tt class="py-lineno"> 787</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-29" class="py-name" targets="Method numdifftools.core.Derivative.derivative()=numdifftools.core.Derivative-class.html#derivative,Method numdifftools.nd_algopy.Derivative.derivative()=numdifftools.nd_algopy.Derivative-class.html#derivative,Method numdifftools.nd_scientific.Derivative.derivative()=numdifftools.nd_scientific.Derivative-class.html#derivative"><a title="numdifftools.core.Derivative.derivative
numdifftools.nd_algopy.Derivative.derivative
numdifftools.nd_scientific.Derivative.derivative" class="py-name" href="#" onclick="return doclink('link-29', 'derivative', 'link-29');">derivative</a></tt><tt class="py-op">(</tt><tt class="py-name">x00</tt><tt class="py-op">)</tt> </tt>
</div><a name="L788"></a><tt class="py-lineno"> 788</tt>  <tt class="py-line"> </tt>
<a name="Derivative.derivative"></a><div id="Derivative.derivative-def"><a name="L789"></a><tt class="py-lineno"> 789</tt> <a class="py-toggle" href="#" id="Derivative.derivative-toggle" onclick="return toggle('Derivative.derivative');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core.Derivative-class.html#derivative">derivative</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x00</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Derivative.derivative-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="Derivative.derivative-expanded"><a name="L790"></a><tt class="py-lineno"> 790</tt>  <tt class="py-line">        <tt class="py-docstring">''' Return estimate of n'th derivative of fun at x0</tt> </tt>
<a name="L791"></a><tt class="py-lineno"> 791</tt>  <tt class="py-line"><tt class="py-docstring">            using romberg extrapolation</tt> </tt>
<a name="L792"></a><tt class="py-lineno"> 792</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L793"></a><tt class="py-lineno"> 793</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-30" class="py-name" targets="Method numdifftools.core._Derivative._initialize()=numdifftools.core._Derivative-class.html#_initialize"><a title="numdifftools.core._Derivative._initialize" class="py-name" href="#" onclick="return doclink('link-30', '_initialize', 'link-30');">_initialize</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L794"></a><tt class="py-lineno"> 794</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-31" class="py-name"><a title="numdifftools.core._Derivative._derivative
numdifftools.nd_algopy._Common._derivative
numdifftools.nd_scientific._Common._derivative" class="py-name" href="#" onclick="return doclink('link-31', '_derivative', 'link-25');">_derivative</a></tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">fun</tt><tt class="py-op">,</tt> <tt class="py-name">x00</tt><tt class="py-op">,</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">step_nom</tt><tt class="py-op">)</tt> </tt>
</div></div><a name="L795"></a><tt class="py-lineno"> 795</tt>  <tt class="py-line"> </tt>
<a name="L796"></a><tt class="py-lineno"> 796</tt>  <tt class="py-line">  </tt>
<a name="Jacobian"></a><div id="Jacobian-def"><a name="L797"></a><tt class="py-lineno"> 797</tt> <a class="py-toggle" href="#" id="Jacobian-toggle" onclick="return toggle('Jacobian');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="numdifftools.core.Jacobian-class.html">Jacobian</a><tt class="py-op">(</tt><tt class="py-base-class">_Derivative</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Jacobian-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="Jacobian-expanded"><a name="L798"></a><tt class="py-lineno"> 798</tt>  <tt class="py-line">    <tt id="link-32" class="py-name" targets="Variable numdifftools.core.Jacobian._jacob_txt=numdifftools.core.Jacobian-class.html#_jacob_txt"><a title="numdifftools.core.Jacobian._jacob_txt" class="py-name" href="#" onclick="return doclink('link-32', '_jacob_txt', 'link-32');">_jacob_txt</a></tt> <tt class="py-op">=</tt> <tt id="link-33" class="py-name"><a title="numdifftools.core._Derivative" class="py-name" href="#" onclick="return doclink('link-33', '_Derivative', 'link-27');">_Derivative</a></tt><tt class="py-op">.</tt><tt id="link-34" class="py-name"><a title="numdifftools.core.Derivative.__doc__
numdifftools.core.Gradient.__doc__
numdifftools.core.Hessdiag.__doc__
numdifftools.core.Hessian.__doc__
numdifftools.core.Jacobian.__doc__" class="py-name" href="#" onclick="return doclink('link-34', '__doc__', 'link-26');">__doc__</a></tt><tt class="py-op">.</tt><tt class="py-name">partition</tt><tt class="py-op">(</tt><tt class="py-string">'\n'</tt><tt class="py-op">)</tt><tt class="py-op">[</tt><tt class="py-number">2</tt><tt class="py-op">]</tt><tt class="py-op">.</tt><tt class="py-name">replace</tt><tt class="py-op">(</tt> </tt>
<a name="L799"></a><tt class="py-lineno"> 799</tt>  <tt class="py-line">    <tt class="py-string">'Integer from 1 to 4 defining derivative order. (Default 1)'</tt><tt class="py-op">,</tt> </tt>
<a name="L800"></a><tt class="py-lineno"> 800</tt>  <tt class="py-line">    <tt class="py-string">'Derivative order is always 1'</tt><tt class="py-op">)</tt> </tt>
<a name="L801"></a><tt class="py-lineno"> 801</tt>  <tt class="py-line">    <tt id="link-35" class="py-name"><a title="numdifftools.core.Derivative.__doc__
numdifftools.core.Gradient.__doc__
numdifftools.core.Hessdiag.__doc__
numdifftools.core.Hessian.__doc__
numdifftools.core.Jacobian.__doc__" class="py-name" href="#" onclick="return doclink('link-35', '__doc__', 'link-26');">__doc__</a></tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt> <tt class="py-comment">#@ReservedAssignment</tt> </tt>
<a name="L802"></a><tt class="py-lineno"> 802</tt>  <tt class="py-line"><tt class="py-string">'''Estimate Jacobian matrix, with error estimate</tt> </tt>
<a name="L803"></a><tt class="py-lineno"> 803</tt>  <tt class="py-line"><tt class="py-string">    '''</tt> <tt class="py-op">+</tt> <tt id="link-36" class="py-name"><a title="numdifftools.core.Jacobian._jacob_txt" class="py-name" href="#" onclick="return doclink('link-36', '_jacob_txt', 'link-32');">_jacob_txt</a></tt> <tt class="py-op">+</tt> <tt class="py-string">'''</tt> </tt>
<a name="L804"></a><tt class="py-lineno"> 804</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L805"></a><tt class="py-lineno"> 805</tt>  <tt class="py-line"><tt class="py-string">    The Jacobian matrix is the matrix of all first-order partial derivatives</tt> </tt>
<a name="L806"></a><tt class="py-lineno"> 806</tt>  <tt class="py-line"><tt class="py-string">    of a vector-valued function.</tt> </tt>
<a name="L807"></a><tt class="py-lineno"> 807</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L808"></a><tt class="py-lineno"> 808</tt>  <tt class="py-line"><tt class="py-string">    Assumptions</tt> </tt>
<a name="L809"></a><tt class="py-lineno"> 809</tt>  <tt class="py-line"><tt class="py-string">    -----------</tt> </tt>
<a name="L810"></a><tt class="py-lineno"> 810</tt>  <tt class="py-line"><tt class="py-string">    fun : (vector valued)</tt> </tt>
<a name="L811"></a><tt class="py-lineno"> 811</tt>  <tt class="py-line"><tt class="py-string">        analytical function to differentiate.</tt> </tt>
<a name="L812"></a><tt class="py-lineno"> 812</tt>  <tt class="py-line"><tt class="py-string">        fun must be a function of the vector or array x0.</tt> </tt>
<a name="L813"></a><tt class="py-lineno"> 813</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L814"></a><tt class="py-lineno"> 814</tt>  <tt class="py-line"><tt class="py-string">    x0 : vector location at which to differentiate fun</tt> </tt>
<a name="L815"></a><tt class="py-lineno"> 815</tt>  <tt class="py-line"><tt class="py-string">        If x0 is an N x M array, then fun is assumed to be</tt> </tt>
<a name="L816"></a><tt class="py-lineno"> 816</tt>  <tt class="py-line"><tt class="py-string">        a function of N*M variables.</tt> </tt>
<a name="L817"></a><tt class="py-lineno"> 817</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L818"></a><tt class="py-lineno"> 818</tt>  <tt class="py-line"><tt class="py-string">    Examples</tt> </tt>
<a name="L819"></a><tt class="py-lineno"> 819</tt>  <tt class="py-line"><tt class="py-string">    --------</tt> </tt>
<a name="L820"></a><tt class="py-lineno"> 820</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; import numpy as np</tt> </tt>
<a name="L821"></a><tt class="py-lineno"> 821</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; import numdifftools as nd</tt> </tt>
<a name="L822"></a><tt class="py-lineno"> 822</tt>  <tt class="py-line"><tt class="py-string">    </tt> </tt>
<a name="L823"></a><tt class="py-lineno"> 823</tt>  <tt class="py-line"><tt class="py-string">    #(nonlinear least squares)</tt> </tt>
<a name="L824"></a><tt class="py-lineno"> 824</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; xdata = np.reshape(np.arange(0,1,0.1),(-1,1))</tt> </tt>
<a name="L825"></a><tt class="py-lineno"> 825</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; ydata = 1+2*np.exp(0.75*xdata)</tt> </tt>
<a name="L826"></a><tt class="py-lineno"> 826</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; fun = lambda c: (c[0]+c[1]*np.exp(c[2]*xdata) - ydata)**2</tt> </tt>
<a name="L827"></a><tt class="py-lineno"> 827</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; Jfun = nd.Jacobian(fun)</tt> </tt>
<a name="L828"></a><tt class="py-lineno"> 828</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; h = Jfun([1., 2., 0.75]) # should be numerically zero</tt> </tt>
<a name="L829"></a><tt class="py-lineno"> 829</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; np.abs(h) &lt; 1e-14</tt> </tt>
<a name="L830"></a><tt class="py-lineno"> 830</tt>  <tt class="py-line"><tt class="py-string">    array([[ True,  True,  True],</tt> </tt>
<a name="L831"></a><tt class="py-lineno"> 831</tt>  <tt class="py-line"><tt class="py-string">           [ True,  True,  True],</tt> </tt>
<a name="L832"></a><tt class="py-lineno"> 832</tt>  <tt class="py-line"><tt class="py-string">           [ True,  True,  True],</tt> </tt>
<a name="L833"></a><tt class="py-lineno"> 833</tt>  <tt class="py-line"><tt class="py-string">           [ True,  True,  True],</tt> </tt>
<a name="L834"></a><tt class="py-lineno"> 834</tt>  <tt class="py-line"><tt class="py-string">           [ True,  True,  True],</tt> </tt>
<a name="L835"></a><tt class="py-lineno"> 835</tt>  <tt class="py-line"><tt class="py-string">           [ True,  True,  True],</tt> </tt>
<a name="L836"></a><tt class="py-lineno"> 836</tt>  <tt class="py-line"><tt class="py-string">           [ True,  True,  True],</tt> </tt>
<a name="L837"></a><tt class="py-lineno"> 837</tt>  <tt class="py-line"><tt class="py-string">           [ True,  True,  True],</tt> </tt>
<a name="L838"></a><tt class="py-lineno"> 838</tt>  <tt class="py-line"><tt class="py-string">           [ True,  True,  True],</tt> </tt>
<a name="L839"></a><tt class="py-lineno"> 839</tt>  <tt class="py-line"><tt class="py-string">           [ True,  True,  True]], dtype=bool)</tt> </tt>
<a name="L840"></a><tt class="py-lineno"> 840</tt>  <tt class="py-line"><tt class="py-string">    </tt> </tt>
<a name="L841"></a><tt class="py-lineno"> 841</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; np.abs(h) &lt;= 2 * Jfun.error_estimate</tt> </tt>
<a name="L842"></a><tt class="py-lineno"> 842</tt>  <tt class="py-line"><tt class="py-string">    array([[ True,  True,  True],</tt> </tt>
<a name="L843"></a><tt class="py-lineno"> 843</tt>  <tt class="py-line"><tt class="py-string">           [ True,  True,  True],</tt> </tt>
<a name="L844"></a><tt class="py-lineno"> 844</tt>  <tt class="py-line"><tt class="py-string">           [ True,  True,  True],</tt> </tt>
<a name="L845"></a><tt class="py-lineno"> 845</tt>  <tt class="py-line"><tt class="py-string">           [ True,  True,  True],</tt> </tt>
<a name="L846"></a><tt class="py-lineno"> 846</tt>  <tt class="py-line"><tt class="py-string">           [ True,  True,  True],</tt> </tt>
<a name="L847"></a><tt class="py-lineno"> 847</tt>  <tt class="py-line"><tt class="py-string">           [ True,  True,  True],</tt> </tt>
<a name="L848"></a><tt class="py-lineno"> 848</tt>  <tt class="py-line"><tt class="py-string">           [ True,  True,  True],</tt> </tt>
<a name="L849"></a><tt class="py-lineno"> 849</tt>  <tt class="py-line"><tt class="py-string">           [ True,  True,  True],</tt> </tt>
<a name="L850"></a><tt class="py-lineno"> 850</tt>  <tt class="py-line"><tt class="py-string">           [ True,  True,  True],</tt> </tt>
<a name="L851"></a><tt class="py-lineno"> 851</tt>  <tt class="py-line"><tt class="py-string">           [ True, False,  True]], dtype=bool)</tt> </tt>
<a name="L852"></a><tt class="py-lineno"> 852</tt>  <tt class="py-line"><tt class="py-string">     </tt> </tt>
<a name="L853"></a><tt class="py-lineno"> 853</tt>  <tt class="py-line"><tt class="py-string">    See also</tt> </tt>
<a name="L854"></a><tt class="py-lineno"> 854</tt>  <tt class="py-line"><tt class="py-string">    --------</tt> </tt>
<a name="L855"></a><tt class="py-lineno"> 855</tt>  <tt class="py-line"><tt class="py-string">    Gradient,</tt> </tt>
<a name="L856"></a><tt class="py-lineno"> 856</tt>  <tt class="py-line"><tt class="py-string">    Derivative,</tt> </tt>
<a name="L857"></a><tt class="py-lineno"> 857</tt>  <tt class="py-line"><tt class="py-string">    Hessdiag,</tt> </tt>
<a name="L858"></a><tt class="py-lineno"> 858</tt>  <tt class="py-line"><tt class="py-string">    Hessian</tt> </tt>
<a name="L859"></a><tt class="py-lineno"> 859</tt>  <tt class="py-line"><tt class="py-string">    '''</tt><tt class="py-op">)</tt> </tt>
<a name="L860"></a><tt class="py-lineno"> 860</tt>  <tt class="py-line">     </tt>
<a name="Jacobian.__call__"></a><div id="Jacobian.__call__-def"><a name="L861"></a><tt class="py-lineno"> 861</tt> <a class="py-toggle" href="#" id="Jacobian.__call__-toggle" onclick="return toggle('Jacobian.__call__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core.Jacobian-class.html#__call__">__call__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x00</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Jacobian.__call__-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="Jacobian.__call__-expanded"><a name="L862"></a><tt class="py-lineno"> 862</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-37" class="py-name" targets="Method numdifftools.core.Jacobian.jacobian()=numdifftools.core.Jacobian-class.html#jacobian,Method numdifftools.nd_algopy.Jacobian.jacobian()=numdifftools.nd_algopy.Jacobian-class.html#jacobian,Method numdifftools.nd_scientific.Jacobian.jacobian()=numdifftools.nd_scientific.Jacobian-class.html#jacobian"><a title="numdifftools.core.Jacobian.jacobian
numdifftools.nd_algopy.Jacobian.jacobian
numdifftools.nd_scientific.Jacobian.jacobian" class="py-name" href="#" onclick="return doclink('link-37', 'jacobian', 'link-37');">jacobian</a></tt><tt class="py-op">(</tt><tt class="py-name">x00</tt><tt class="py-op">)</tt> </tt>
</div><a name="L863"></a><tt class="py-lineno"> 863</tt>  <tt class="py-line"> </tt>
<a name="Jacobian.jacobian"></a><div id="Jacobian.jacobian-def"><a name="L864"></a><tt class="py-lineno"> 864</tt> <a class="py-toggle" href="#" id="Jacobian.jacobian-toggle" onclick="return toggle('Jacobian.jacobian');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core.Jacobian-class.html#jacobian">jacobian</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x00</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Jacobian.jacobian-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="Jacobian.jacobian-expanded"><a name="L865"></a><tt class="py-lineno"> 865</tt>  <tt class="py-line">        <tt class="py-docstring">'''</tt> </tt>
<a name="L866"></a><tt class="py-lineno"> 866</tt>  <tt class="py-line"><tt class="py-docstring">        Return Jacobian matrix of a vector valued function of n variables</tt> </tt>
<a name="L867"></a><tt class="py-lineno"> 867</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L868"></a><tt class="py-lineno"> 868</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L869"></a><tt class="py-lineno"> 869</tt>  <tt class="py-line"><tt class="py-docstring">        Parameter</tt> </tt>
<a name="L870"></a><tt class="py-lineno"> 870</tt>  <tt class="py-line"><tt class="py-docstring">        ---------</tt> </tt>
<a name="L871"></a><tt class="py-lineno"> 871</tt>  <tt class="py-line"><tt class="py-docstring">        x0 : vector</tt> </tt>
<a name="L872"></a><tt class="py-lineno"> 872</tt>  <tt class="py-line"><tt class="py-docstring">            location at which to differentiate fun.</tt> </tt>
<a name="L873"></a><tt class="py-lineno"> 873</tt>  <tt class="py-line"><tt class="py-docstring">            If x0 is an nxm array, then fun is assumed to be</tt> </tt>
<a name="L874"></a><tt class="py-lineno"> 874</tt>  <tt class="py-line"><tt class="py-docstring">            a function of n*m variables.</tt> </tt>
<a name="L875"></a><tt class="py-lineno"> 875</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L876"></a><tt class="py-lineno"> 876</tt>  <tt class="py-line"><tt class="py-docstring">        Member variable used</tt> </tt>
<a name="L877"></a><tt class="py-lineno"> 877</tt>  <tt class="py-line"><tt class="py-docstring">        --------------------</tt> </tt>
<a name="L878"></a><tt class="py-lineno"> 878</tt>  <tt class="py-line"><tt class="py-docstring">        fun : (vector valued) analytical function to differentiate.</tt> </tt>
<a name="L879"></a><tt class="py-lineno"> 879</tt>  <tt class="py-line"><tt class="py-docstring">                fun must be a function of the vector or array x0.</tt> </tt>
<a name="L880"></a><tt class="py-lineno"> 880</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L881"></a><tt class="py-lineno"> 881</tt>  <tt class="py-line"><tt class="py-docstring">        Returns</tt> </tt>
<a name="L882"></a><tt class="py-lineno"> 882</tt>  <tt class="py-line"><tt class="py-docstring">        -------</tt> </tt>
<a name="L883"></a><tt class="py-lineno"> 883</tt>  <tt class="py-line"><tt class="py-docstring">        jac : array-like</tt> </tt>
<a name="L884"></a><tt class="py-lineno"> 884</tt>  <tt class="py-line"><tt class="py-docstring">           first partial derivatives of fun. Assuming that x0</tt> </tt>
<a name="L885"></a><tt class="py-lineno"> 885</tt>  <tt class="py-line"><tt class="py-docstring">           is a vector of length p and fun returns a vector</tt> </tt>
<a name="L886"></a><tt class="py-lineno"> 886</tt>  <tt class="py-line"><tt class="py-docstring">           of length n, then jac will be an array of size (n,p)</tt> </tt>
<a name="L887"></a><tt class="py-lineno"> 887</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L888"></a><tt class="py-lineno"> 888</tt>  <tt class="py-line"><tt class="py-docstring">        err - vector</tt> </tt>
<a name="L889"></a><tt class="py-lineno"> 889</tt>  <tt class="py-line"><tt class="py-docstring">            of error estimates corresponding to each partial</tt> </tt>
<a name="L890"></a><tt class="py-lineno"> 890</tt>  <tt class="py-line"><tt class="py-docstring">            derivative in jac.</tt> </tt>
<a name="L891"></a><tt class="py-lineno"> 891</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L892"></a><tt class="py-lineno"> 892</tt>  <tt class="py-line"><tt class="py-docstring">        See also</tt> </tt>
<a name="L893"></a><tt class="py-lineno"> 893</tt>  <tt class="py-line"><tt class="py-docstring">        --------</tt> </tt>
<a name="L894"></a><tt class="py-lineno"> 894</tt>  <tt class="py-line"><tt class="py-docstring">        Derivative,</tt> </tt>
<a name="L895"></a><tt class="py-lineno"> 895</tt>  <tt class="py-line"><tt class="py-docstring">        Gradient,</tt> </tt>
<a name="L896"></a><tt class="py-lineno"> 896</tt>  <tt class="py-line"><tt class="py-docstring">        Hessian,</tt> </tt>
<a name="L897"></a><tt class="py-lineno"> 897</tt>  <tt class="py-line"><tt class="py-docstring">        Hessdiag</tt> </tt>
<a name="L898"></a><tt class="py-lineno"> 898</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L899"></a><tt class="py-lineno"> 899</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">n</tt> <tt class="py-op">=</tt> <tt class="py-number">1</tt> </tt>
<a name="L900"></a><tt class="py-lineno"> 900</tt>  <tt class="py-line">        <tt class="py-name">fun</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">fun</tt> </tt>
<a name="L901"></a><tt class="py-lineno"> 901</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-38" class="py-name"><a title="numdifftools.core._Derivative._initialize" class="py-name" href="#" onclick="return doclink('link-38', '_initialize', 'link-30');">_initialize</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L902"></a><tt class="py-lineno"> 902</tt>  <tt class="py-line"> </tt>
<a name="L903"></a><tt class="py-lineno"> 903</tt>  <tt class="py-line">        <tt class="py-name">zeros</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt> </tt>
<a name="L904"></a><tt class="py-lineno"> 904</tt>  <tt class="py-line">        <tt class="py-name">newaxis</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">newaxis</tt> </tt>
<a name="L905"></a><tt class="py-lineno"> 905</tt>  <tt class="py-line">        <tt class="py-name">x0</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">atleast_1d</tt><tt class="py-op">(</tt><tt class="py-name">x00</tt><tt class="py-op">)</tt> </tt>
<a name="L906"></a><tt class="py-lineno"> 906</tt>  <tt class="py-line">        <tt class="py-name">nx</tt> <tt class="py-op">=</tt> <tt class="py-name">x0</tt><tt class="py-op">.</tt><tt class="py-name">size</tt> </tt>
<a name="L907"></a><tt class="py-lineno"> 907</tt>  <tt class="py-line"> </tt>
<a name="L908"></a><tt class="py-lineno"> 908</tt>  <tt class="py-line"> </tt>
<a name="L909"></a><tt class="py-lineno"> 909</tt>  <tt class="py-line">        <tt class="py-comment"># get fun at the center point</tt> </tt>
<a name="L910"></a><tt class="py-lineno"> 910</tt>  <tt class="py-line">        <tt class="py-name">f0</tt> <tt class="py-op">=</tt> <tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">)</tt> </tt>
<a name="L911"></a><tt class="py-lineno"> 911</tt>  <tt class="py-line">        <tt class="py-name">f0</tt> <tt class="py-op">=</tt> <tt class="py-name">f0</tt><tt class="py-op">.</tt><tt class="py-name">ravel</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L912"></a><tt class="py-lineno"> 912</tt>  <tt class="py-line">        <tt class="py-name">n</tt> <tt class="py-op">=</tt> <tt class="py-name">f0</tt><tt class="py-op">.</tt><tt class="py-name">size</tt> </tt>
<a name="L913"></a><tt class="py-lineno"> 913</tt>  <tt class="py-line"> </tt>
<a name="L914"></a><tt class="py-lineno"> 914</tt>  <tt class="py-line">        <tt class="py-name">jac</tt> <tt class="py-op">=</tt> <tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">n</tt><tt class="py-op">,</tt> <tt class="py-name">nx</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L915"></a><tt class="py-lineno"> 915</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">n</tt> <tt class="py-op">==</tt> <tt class="py-number">0</tt> <tt class="py-op">:</tt> </tt>
<a name="L916"></a><tt class="py-lineno"> 916</tt>  <tt class="py-line">            <tt class="py-comment"># empty begets empty</tt> </tt>
<a name="L917"></a><tt class="py-lineno"> 917</tt>  <tt class="py-line">            <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">error_estimate</tt> <tt class="py-op">=</tt> <tt class="py-name">jac</tt> </tt>
<a name="L918"></a><tt class="py-lineno"> 918</tt>  <tt class="py-line">            <tt class="py-keyword">return</tt> <tt class="py-name">jac</tt> </tt>
<a name="L919"></a><tt class="py-lineno"> 919</tt>  <tt class="py-line"> </tt>
<a name="L920"></a><tt class="py-lineno"> 920</tt>  <tt class="py-line">        <tt class="py-name">delta</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_delta</tt> </tt>
<a name="L921"></a><tt class="py-lineno"> 921</tt>  <tt class="py-line">        <tt class="py-name">nsteps</tt> <tt class="py-op">=</tt> <tt class="py-name">delta</tt><tt class="py-op">.</tt><tt class="py-name">size</tt> </tt>
<a name="L922"></a><tt class="py-lineno"> 922</tt>  <tt class="py-line"> </tt>
<a name="L923"></a><tt class="py-lineno"> 923</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">step_nom</tt> <tt class="py-op">==</tt> <tt class="py-name">None</tt> <tt class="py-op">:</tt> </tt>
<a name="L924"></a><tt class="py-lineno"> 924</tt>  <tt class="py-line">            <tt class="py-name">stepNom</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">maximum</tt><tt class="py-op">(</tt><tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">abs</tt><tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-number">0.02</tt><tt class="py-op">)</tt> </tt>
<a name="L925"></a><tt class="py-lineno"> 925</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L926"></a><tt class="py-lineno"> 926</tt>  <tt class="py-line">            <tt class="py-name">stepNom</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">step_nom</tt> </tt>
<a name="L927"></a><tt class="py-lineno"> 927</tt>  <tt class="py-line"> </tt>
<a name="L928"></a><tt class="py-lineno"> 928</tt>  <tt class="py-line">        <tt class="py-name">err</tt> <tt class="py-op">=</tt> <tt class="py-name">jac</tt><tt class="py-op">.</tt><tt class="py-name">copy</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L929"></a><tt class="py-lineno"> 929</tt>  <tt class="py-line">        <tt class="py-name">finaldelta</tt> <tt class="py-op">=</tt> <tt class="py-name">jac</tt><tt class="py-op">.</tt><tt class="py-name">copy</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L930"></a><tt class="py-lineno"> 930</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-name">i</tt> <tt class="py-keyword">in</tt> <tt class="py-name">range</tt><tt class="py-op">(</tt><tt class="py-name">nx</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L931"></a><tt class="py-lineno"> 931</tt>  <tt class="py-line">            <tt class="py-name">x0_i</tt> <tt class="py-op">=</tt> <tt class="py-name">x0</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt> </tt>
<a name="L932"></a><tt class="py-lineno"> 932</tt>  <tt class="py-line">            <tt class="py-name">h</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-number">1.0</tt> <tt class="py-op">*</tt> <tt class="py-name">stepNom</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">delta</tt> </tt>
<a name="L933"></a><tt class="py-lineno"> 933</tt>  <tt class="py-line"> </tt>
<a name="L934"></a><tt class="py-lineno"> 934</tt>  <tt class="py-line">            <tt class="py-comment"># evaluate at each step, centered around x0_i</tt> </tt>
<a name="L935"></a><tt class="py-lineno"> 935</tt>  <tt class="py-line">            <tt class="py-comment"># difference to give a second order estimate</tt> </tt>
<a name="L936"></a><tt class="py-lineno"> 936</tt>  <tt class="py-line">            <tt class="py-name">fdel</tt> <tt class="py-op">=</tt> <tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">n</tt><tt class="py-op">,</tt> <tt class="py-name">nsteps</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L937"></a><tt class="py-lineno"> 937</tt>  <tt class="py-line">            <tt class="py-name">xp</tt> <tt class="py-op">=</tt> <tt class="py-name">x0</tt><tt class="py-op">.</tt><tt class="py-name">copy</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L938"></a><tt class="py-lineno"> 938</tt>  <tt class="py-line">            <tt class="py-name">xm</tt> <tt class="py-op">=</tt> <tt class="py-name">x0</tt><tt class="py-op">.</tt><tt class="py-name">copy</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L939"></a><tt class="py-lineno"> 939</tt>  <tt class="py-line">            <tt class="py-keyword">for</tt> <tt class="py-name">j</tt> <tt class="py-keyword">in</tt> <tt class="py-name">range</tt><tt class="py-op">(</tt><tt class="py-name">nsteps</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L940"></a><tt class="py-lineno"> 940</tt>  <tt class="py-line">                <tt class="py-name">xp</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">x0_i</tt> <tt class="py-op">+</tt> <tt class="py-name">h</tt><tt class="py-op">[</tt><tt class="py-name">j</tt><tt class="py-op">]</tt> </tt>
<a name="L941"></a><tt class="py-lineno"> 941</tt>  <tt class="py-line">                <tt class="py-name">xm</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">x0_i</tt> <tt class="py-op">-</tt> <tt class="py-name">h</tt><tt class="py-op">[</tt><tt class="py-name">j</tt><tt class="py-op">]</tt> </tt>
<a name="L942"></a><tt class="py-lineno"> 942</tt>  <tt class="py-line">                <tt class="py-name">fdif</tt> <tt class="py-op">=</tt> <tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">xp</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">xm</tt><tt class="py-op">)</tt> </tt>
<a name="L943"></a><tt class="py-lineno"> 943</tt>  <tt class="py-line">                <tt class="py-name">fdel</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt> <tt class="py-name">j</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">fdif</tt><tt class="py-op">.</tt><tt class="py-name">ravel</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L944"></a><tt class="py-lineno"> 944</tt>  <tt class="py-line"> </tt>
<a name="L945"></a><tt class="py-lineno"> 945</tt>  <tt class="py-line"> </tt>
<a name="L946"></a><tt class="py-lineno"> 946</tt>  <tt class="py-line">            <tt class="py-comment"># these are pure second order estimates of the</tt> </tt>
<a name="L947"></a><tt class="py-lineno"> 947</tt>  <tt class="py-line">            <tt class="py-comment"># first derivative, for each trial delta.</tt> </tt>
<a name="L948"></a><tt class="py-lineno"> 948</tt>  <tt class="py-line">            <tt class="py-name">derest</tt> <tt class="py-op">=</tt> <tt class="py-name">fdel</tt> <tt class="py-op">*</tt> <tt class="py-number">0.5</tt> <tt class="py-op">/</tt> <tt class="py-name">h</tt><tt class="py-op">[</tt><tt class="py-name">newaxis</tt><tt class="py-op">,</tt> <tt class="py-op">:</tt><tt class="py-op">]</tt> </tt>
<a name="L949"></a><tt class="py-lineno"> 949</tt>  <tt class="py-line"> </tt>
<a name="L950"></a><tt class="py-lineno"> 950</tt>  <tt class="py-line">            <tt class="py-comment"># The error term on these estimates has a second order</tt> </tt>
<a name="L951"></a><tt class="py-lineno"> 951</tt>  <tt class="py-line">            <tt class="py-comment"># component, but also some 4th and 6th order terms in it.</tt> </tt>
<a name="L952"></a><tt class="py-lineno"> 952</tt>  <tt class="py-line">            <tt class="py-comment"># Use Romberg extrapolation to improve the estimates to</tt> </tt>
<a name="L953"></a><tt class="py-lineno"> 953</tt>  <tt class="py-line">            <tt class="py-comment"># 6th order, as well as to provide the error estimate.</tt> </tt>
<a name="L954"></a><tt class="py-lineno"> 954</tt>  <tt class="py-line"> </tt>
<a name="L955"></a><tt class="py-lineno"> 955</tt>  <tt class="py-line">            <tt class="py-comment"># loop here, as rombextrap coupled with the trimming</tt> </tt>
<a name="L956"></a><tt class="py-lineno"> 956</tt>  <tt class="py-line">            <tt class="py-comment"># will get complicated otherwise.</tt> </tt>
<a name="L957"></a><tt class="py-lineno"> 957</tt>  <tt class="py-line">            <tt class="py-keyword">for</tt> <tt class="py-name">j</tt> <tt class="py-keyword">in</tt> <tt class="py-name">range</tt><tt class="py-op">(</tt><tt class="py-name">n</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L958"></a><tt class="py-lineno"> 958</tt>  <tt class="py-line">                <tt class="py-name">der_romb</tt><tt class="py-op">,</tt> <tt class="py-name">errest</tt><tt class="py-op">,</tt> <tt class="py-name">h1</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-39" class="py-name"><a title="numdifftools.core._Derivative._romb_extrap" class="py-name" href="#" onclick="return doclink('link-39', '_romb_extrap', 'link-9');">_romb_extrap</a></tt><tt class="py-op">(</tt><tt class="py-name">derest</tt><tt class="py-op">[</tt><tt class="py-name">j</tt><tt class="py-op">,</tt> <tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt><tt class="py-op">)</tt> </tt>
<a name="L959"></a><tt class="py-lineno"> 959</tt>  <tt class="py-line"> </tt>
<a name="L960"></a><tt class="py-lineno"> 960</tt>  <tt class="py-line">                <tt class="py-comment"># trim off 3 estimates at each end of the scale</tt> </tt>
<a name="L961"></a><tt class="py-lineno"> 961</tt>  <tt class="py-line"> </tt>
<a name="L962"></a><tt class="py-lineno"> 962</tt>  <tt class="py-line">                <tt class="py-name">tags</tt> <tt class="py-op">=</tt> <tt class="py-name">der_romb</tt><tt class="py-op">.</tt><tt class="py-name">argsort</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L963"></a><tt class="py-lineno"> 963</tt>  <tt class="py-line">                <tt class="py-name">tags</tt> <tt class="py-op">=</tt> <tt class="py-name">tags</tt><tt class="py-op">[</tt><tt class="py-number">3</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">3</tt><tt class="py-op">]</tt> </tt>
<a name="L964"></a><tt class="py-lineno"> 964</tt>  <tt class="py-line">                <tt class="py-name">der_romb</tt> <tt class="py-op">=</tt> <tt class="py-name">der_romb</tt><tt class="py-op">[</tt><tt class="py-name">tags</tt><tt class="py-op">]</tt> </tt>
<a name="L965"></a><tt class="py-lineno"> 965</tt>  <tt class="py-line"> </tt>
<a name="L966"></a><tt class="py-lineno"> 966</tt>  <tt class="py-line">                <tt class="py-name">errest</tt> <tt class="py-op">=</tt> <tt class="py-name">errest</tt><tt class="py-op">[</tt><tt class="py-name">tags</tt><tt class="py-op">]</tt> </tt>
<a name="L967"></a><tt class="py-lineno"> 967</tt>  <tt class="py-line">                <tt class="py-name">trimdelta</tt> <tt class="py-op">=</tt> <tt class="py-name">h1</tt><tt class="py-op">[</tt><tt class="py-name">tags</tt><tt class="py-op">]</tt> </tt>
<a name="L968"></a><tt class="py-lineno"> 968</tt>  <tt class="py-line"> </tt>
<a name="L969"></a><tt class="py-lineno"> 969</tt>  <tt class="py-line">                <tt class="py-comment"># now pick the estimate with the lowest predicted error</tt> </tt>
<a name="L970"></a><tt class="py-lineno"> 970</tt>  <tt class="py-line">                <tt class="py-name">ind</tt> <tt class="py-op">=</tt> <tt class="py-name">errest</tt><tt class="py-op">.</tt><tt class="py-name">argmin</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L971"></a><tt class="py-lineno"> 971</tt>  <tt class="py-line">                <tt class="py-name">err</tt><tt class="py-op">[</tt><tt class="py-name">j</tt><tt class="py-op">,</tt> <tt class="py-name">i</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">errest</tt><tt class="py-op">[</tt><tt class="py-name">ind</tt><tt class="py-op">]</tt> </tt>
<a name="L972"></a><tt class="py-lineno"> 972</tt>  <tt class="py-line">                <tt class="py-name">finaldelta</tt><tt class="py-op">[</tt><tt class="py-name">j</tt><tt class="py-op">,</tt> <tt class="py-name">i</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">trimdelta</tt><tt class="py-op">[</tt><tt class="py-name">ind</tt><tt class="py-op">]</tt> </tt>
<a name="L973"></a><tt class="py-lineno"> 973</tt>  <tt class="py-line">                <tt class="py-name">jac</tt><tt class="py-op">[</tt><tt class="py-name">j</tt><tt class="py-op">,</tt> <tt class="py-name">i</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">der_romb</tt><tt class="py-op">[</tt><tt class="py-name">ind</tt><tt class="py-op">]</tt> </tt>
<a name="L974"></a><tt class="py-lineno"> 974</tt>  <tt class="py-line"> </tt>
<a name="L975"></a><tt class="py-lineno"> 975</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">finaldelta</tt> <tt class="py-op">=</tt> <tt class="py-name">finaldelta</tt> </tt>
<a name="L976"></a><tt class="py-lineno"> 976</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">error_estimate</tt> <tt class="py-op">=</tt> <tt class="py-name">err</tt> </tt>
<a name="L977"></a><tt class="py-lineno"> 977</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">jac</tt> </tt>
</div></div><a name="L978"></a><tt class="py-lineno"> 978</tt>  <tt class="py-line"> </tt>
<a name="L979"></a><tt class="py-lineno"> 979</tt>  <tt class="py-line"> </tt>
<a name="Gradient"></a><div id="Gradient-def"><a name="L980"></a><tt class="py-lineno"> 980</tt> <a class="py-toggle" href="#" id="Gradient-toggle" onclick="return toggle('Gradient');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="numdifftools.core.Gradient-class.html">Gradient</a><tt class="py-op">(</tt><tt class="py-base-class">_PartialDerivative</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Gradient-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="Gradient-expanded"><a name="L981"></a><tt class="py-lineno"> 981</tt>  <tt class="py-line">     </tt>
<a name="L982"></a><tt class="py-lineno"> 982</tt>  <tt class="py-line">    <tt id="link-40" class="py-name" targets="Variable numdifftools.core.Gradient._grad_txt=numdifftools.core.Gradient-class.html#_grad_txt"><a title="numdifftools.core.Gradient._grad_txt" class="py-name" href="#" onclick="return doclink('link-40', '_grad_txt', 'link-40');">_grad_txt</a></tt> <tt class="py-op">=</tt> <tt id="link-41" class="py-name"><a title="numdifftools.core._Derivative" class="py-name" href="#" onclick="return doclink('link-41', '_Derivative', 'link-27');">_Derivative</a></tt><tt class="py-op">.</tt><tt id="link-42" class="py-name"><a title="numdifftools.core.Derivative.__doc__
numdifftools.core.Gradient.__doc__
numdifftools.core.Hessdiag.__doc__
numdifftools.core.Hessian.__doc__
numdifftools.core.Jacobian.__doc__" class="py-name" href="#" onclick="return doclink('link-42', '__doc__', 'link-26');">__doc__</a></tt><tt class="py-op">.</tt><tt class="py-name">partition</tt><tt class="py-op">(</tt><tt class="py-string">'\n'</tt><tt class="py-op">)</tt><tt class="py-op">[</tt><tt class="py-number">2</tt><tt class="py-op">]</tt><tt class="py-op">.</tt><tt class="py-name">replace</tt><tt class="py-op">(</tt> </tt>
<a name="L983"></a><tt class="py-lineno"> 983</tt>  <tt class="py-line">        <tt class="py-string">'Integer from 1 to 4 defining derivative order. (Default 1)'</tt><tt class="py-op">,</tt> </tt>
<a name="L984"></a><tt class="py-lineno"> 984</tt>  <tt class="py-line">        <tt class="py-string">'Derivative order is always 1'</tt><tt class="py-op">)</tt> </tt>
<a name="L985"></a><tt class="py-lineno"> 985</tt>  <tt class="py-line">    <tt id="link-43" class="py-name"><a title="numdifftools.core.Derivative.__doc__
numdifftools.core.Gradient.__doc__
numdifftools.core.Hessdiag.__doc__
numdifftools.core.Hessian.__doc__
numdifftools.core.Jacobian.__doc__" class="py-name" href="#" onclick="return doclink('link-43', '__doc__', 'link-26');">__doc__</a></tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt> <tt class="py-comment">#@ReservedAssignment</tt> </tt>
<a name="L986"></a><tt class="py-lineno"> 986</tt>  <tt class="py-line">    <tt class="py-string">'''Estimate gradient of fun at x0, with error estimate</tt> </tt>
<a name="L987"></a><tt class="py-lineno"> 987</tt>  <tt class="py-line"><tt class="py-string">    '''</tt> <tt class="py-op">+</tt> <tt id="link-44" class="py-name"><a title="numdifftools.core.Gradient._grad_txt" class="py-name" href="#" onclick="return doclink('link-44', '_grad_txt', 'link-40');">_grad_txt</a></tt> <tt class="py-op">+</tt> <tt class="py-string">'''</tt> </tt>
<a name="L988"></a><tt class="py-lineno"> 988</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L989"></a><tt class="py-lineno"> 989</tt>  <tt class="py-line"><tt class="py-string">    Assumptions</tt> </tt>
<a name="L990"></a><tt class="py-lineno"> 990</tt>  <tt class="py-line"><tt class="py-string">    -----------</tt> </tt>
<a name="L991"></a><tt class="py-lineno"> 991</tt>  <tt class="py-line"><tt class="py-string">    fun : SCALAR analytical function to differentiate.</tt> </tt>
<a name="L992"></a><tt class="py-lineno"> 992</tt>  <tt class="py-line"><tt class="py-string">        fun must be a function of the vector or array x0,</tt> </tt>
<a name="L993"></a><tt class="py-lineno"> 993</tt>  <tt class="py-line"><tt class="py-string">        but it needs not to be vectorized.</tt> </tt>
<a name="L994"></a><tt class="py-lineno"> 994</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L995"></a><tt class="py-lineno"> 995</tt>  <tt class="py-line"><tt class="py-string">    x0 : vector location at which to differentiate fun</tt> </tt>
<a name="L996"></a><tt class="py-lineno"> 996</tt>  <tt class="py-line"><tt class="py-string">        If x0 is an N x M array, then fun is assumed to be</tt> </tt>
<a name="L997"></a><tt class="py-lineno"> 997</tt>  <tt class="py-line"><tt class="py-string">        a function of N*M variables.</tt> </tt>
<a name="L998"></a><tt class="py-lineno"> 998</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L999"></a><tt class="py-lineno"> 999</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1000"></a><tt class="py-lineno">1000</tt>  <tt class="py-line"><tt class="py-string">    Examples</tt> </tt>
<a name="L1001"></a><tt class="py-lineno">1001</tt>  <tt class="py-line"><tt class="py-string">    --------</tt> </tt>
<a name="L1002"></a><tt class="py-lineno">1002</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; import numpy as np</tt> </tt>
<a name="L1003"></a><tt class="py-lineno">1003</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; import numdifftools as nd</tt> </tt>
<a name="L1004"></a><tt class="py-lineno">1004</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; fun = lambda x: np.sum(x**2)</tt> </tt>
<a name="L1005"></a><tt class="py-lineno">1005</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; dfun = nd.Gradient(fun)</tt> </tt>
<a name="L1006"></a><tt class="py-lineno">1006</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; dfun([1,2,3])</tt> </tt>
<a name="L1007"></a><tt class="py-lineno">1007</tt>  <tt class="py-line"><tt class="py-string">    array([ 2.,  4.,  6.])</tt> </tt>
<a name="L1008"></a><tt class="py-lineno">1008</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1009"></a><tt class="py-lineno">1009</tt>  <tt class="py-line"><tt class="py-string">    # At [x,y] = [1,1], compute the numerical gradient</tt> </tt>
<a name="L1010"></a><tt class="py-lineno">1010</tt>  <tt class="py-line"><tt class="py-string">    # of the function sin(x-y) + y*exp(x)</tt> </tt>
<a name="L1011"></a><tt class="py-lineno">1011</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1012"></a><tt class="py-lineno">1012</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; sin = np.sin; exp = np.exp</tt> </tt>
<a name="L1013"></a><tt class="py-lineno">1013</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; z = lambda xy: sin(xy[0]-xy[1]) + xy[1]*exp(xy[0])</tt> </tt>
<a name="L1014"></a><tt class="py-lineno">1014</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; dz = Gradient(z)</tt> </tt>
<a name="L1015"></a><tt class="py-lineno">1015</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; grad2 = dz([1, 1])</tt> </tt>
<a name="L1016"></a><tt class="py-lineno">1016</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; grad2</tt> </tt>
<a name="L1017"></a><tt class="py-lineno">1017</tt>  <tt class="py-line"><tt class="py-string">    array([ 3.71828183,  1.71828183])</tt> </tt>
<a name="L1018"></a><tt class="py-lineno">1018</tt>  <tt class="py-line"><tt class="py-string">     </tt> </tt>
<a name="L1019"></a><tt class="py-lineno">1019</tt>  <tt class="py-line"><tt class="py-string">    # At the global minimizer (1,1) of the Rosenbrock function,</tt> </tt>
<a name="L1020"></a><tt class="py-lineno">1020</tt>  <tt class="py-line"><tt class="py-string">    # compute the gradient. It should be essentially zero.</tt> </tt>
<a name="L1021"></a><tt class="py-lineno">1021</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1022"></a><tt class="py-lineno">1022</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; rosen = lambda x : (1-x[0])**2 + 105.*(x[1]-x[0]**2)**2</tt> </tt>
<a name="L1023"></a><tt class="py-lineno">1023</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; rd = Gradient(rosen)</tt> </tt>
<a name="L1024"></a><tt class="py-lineno">1024</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; grad3 = rd([1,1])</tt> </tt>
<a name="L1025"></a><tt class="py-lineno">1025</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; grad3</tt> </tt>
<a name="L1026"></a><tt class="py-lineno">1026</tt>  <tt class="py-line"><tt class="py-string">    array([ 0.,  0.])</tt> </tt>
<a name="L1027"></a><tt class="py-lineno">1027</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; np.abs(grad3)&lt;=rd.error_estimate</tt> </tt>
<a name="L1028"></a><tt class="py-lineno">1028</tt>  <tt class="py-line"><tt class="py-string">    array([ True,  True], dtype=bool)</tt> </tt>
<a name="L1029"></a><tt class="py-lineno">1029</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1030"></a><tt class="py-lineno">1030</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1031"></a><tt class="py-lineno">1031</tt>  <tt class="py-line"><tt class="py-string">    See also</tt> </tt>
<a name="L1032"></a><tt class="py-lineno">1032</tt>  <tt class="py-line"><tt class="py-string">    --------</tt> </tt>
<a name="L1033"></a><tt class="py-lineno">1033</tt>  <tt class="py-line"><tt class="py-string">    Derivative, Hessdiag, Hessian, Jacobian</tt> </tt>
<a name="L1034"></a><tt class="py-lineno">1034</tt>  <tt class="py-line"><tt class="py-string">    '''</tt><tt class="py-op">)</tt> </tt>
<a name="L1035"></a><tt class="py-lineno">1035</tt>  <tt class="py-line">       </tt>
<a name="Gradient.__call__"></a><div id="Gradient.__call__-def"><a name="L1036"></a><tt class="py-lineno">1036</tt> <a class="py-toggle" href="#" id="Gradient.__call__-toggle" onclick="return toggle('Gradient.__call__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core.Gradient-class.html#__call__">__call__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x00</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Gradient.__call__-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="Gradient.__call__-expanded"><a name="L1037"></a><tt class="py-lineno">1037</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-45" class="py-name" targets="Method numdifftools.core.Gradient.gradient()=numdifftools.core.Gradient-class.html#gradient,Method numdifftools.nd_algopy.Gradient.gradient()=numdifftools.nd_algopy.Gradient-class.html#gradient,Method numdifftools.nd_scientific.Gradient.gradient()=numdifftools.nd_scientific.Gradient-class.html#gradient"><a title="numdifftools.core.Gradient.gradient
numdifftools.nd_algopy.Gradient.gradient
numdifftools.nd_scientific.Gradient.gradient" class="py-name" href="#" onclick="return doclink('link-45', 'gradient', 'link-45');">gradient</a></tt><tt class="py-op">(</tt><tt class="py-name">x00</tt><tt class="py-op">)</tt> </tt>
</div><a name="Gradient.gradient"></a><div id="Gradient.gradient-def"><a name="L1038"></a><tt class="py-lineno">1038</tt> <a class="py-toggle" href="#" id="Gradient.gradient-toggle" onclick="return toggle('Gradient.gradient');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core.Gradient-class.html#gradient">gradient</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x00</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Gradient.gradient-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="Gradient.gradient-expanded"><a name="L1039"></a><tt class="py-lineno">1039</tt>  <tt class="py-line">        <tt class="py-docstring">''' Gradient vector of an analytical function of n variables</tt> </tt>
<a name="L1040"></a><tt class="py-lineno">1040</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L1041"></a><tt class="py-lineno">1041</tt>  <tt class="py-line"><tt class="py-docstring">         CALL: [grad,err,finaldelta] = fun.gradient(x0)</tt> </tt>
<a name="L1042"></a><tt class="py-lineno">1042</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L1043"></a><tt class="py-lineno">1043</tt>  <tt class="py-line"><tt class="py-docstring">          grad = first partial derivatives of fun evaluated at x0.    Size 1 x N</tt> </tt>
<a name="L1044"></a><tt class="py-lineno">1044</tt>  <tt class="py-line"><tt class="py-docstring">          err  = error estimates corresponding to each value in grad. Size 1 x N</tt> </tt>
<a name="L1045"></a><tt class="py-lineno">1045</tt>  <tt class="py-line"><tt class="py-docstring">          finaldelta = vector of final step sizes chosen for each partial derivative.</tt> </tt>
<a name="L1046"></a><tt class="py-lineno">1046</tt>  <tt class="py-line"><tt class="py-docstring">          fun  = analytical function to differentiate. fun must</tt> </tt>
<a name="L1047"></a><tt class="py-lineno">1047</tt>  <tt class="py-line"><tt class="py-docstring">                be a function of the vector or array x0.</tt> </tt>
<a name="L1048"></a><tt class="py-lineno">1048</tt>  <tt class="py-line"><tt class="py-docstring">          x0   = vector location at which to differentiate fun</tt> </tt>
<a name="L1049"></a><tt class="py-lineno">1049</tt>  <tt class="py-line"><tt class="py-docstring">                If x0 is an nxm array, then fun is assumed to be</tt> </tt>
<a name="L1050"></a><tt class="py-lineno">1050</tt>  <tt class="py-line"><tt class="py-docstring">                a function of N = n*m variables.</tt> </tt>
<a name="L1051"></a><tt class="py-lineno">1051</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L1052"></a><tt class="py-lineno">1052</tt>  <tt class="py-line"><tt class="py-docstring">         GRADEST estimate first partial derivatives of fun evaluated at x0.</tt> </tt>
<a name="L1053"></a><tt class="py-lineno">1053</tt>  <tt class="py-line"><tt class="py-docstring">         GRADEST uses derivest to provide both derivative estimates</tt> </tt>
<a name="L1054"></a><tt class="py-lineno">1054</tt>  <tt class="py-line"><tt class="py-docstring">         and error estimates. fun needs not be vectorized.</tt> </tt>
<a name="L1055"></a><tt class="py-lineno">1055</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L1056"></a><tt class="py-lineno">1056</tt>  <tt class="py-line"><tt class="py-docstring">         Examples</tt> </tt>
<a name="L1057"></a><tt class="py-lineno">1057</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L1058"></a><tt class="py-lineno">1058</tt>  <tt class="py-line"><tt class="py-docstring">          #[grad,err] = gradest(@(x) sum(x.^2),[1 2 3]) #  grad = [ 2,4, 6]</tt> </tt>
<a name="L1059"></a><tt class="py-lineno">1059</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L1060"></a><tt class="py-lineno">1060</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L1061"></a><tt class="py-lineno">1061</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">n</tt> <tt class="py-op">=</tt> <tt class="py-number">1</tt> </tt>
<a name="L1062"></a><tt class="py-lineno">1062</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">vectorized</tt> <tt class="py-op">=</tt> <tt class="py-name">False</tt> </tt>
<a name="L1063"></a><tt class="py-lineno">1063</tt>  <tt class="py-line"> </tt>
<a name="L1064"></a><tt class="py-lineno">1064</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-46" class="py-name"><a title="numdifftools.core._Derivative._initialize" class="py-name" href="#" onclick="return doclink('link-46', '_initialize', 'link-30');">_initialize</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L1065"></a><tt class="py-lineno">1065</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-47" class="py-name" targets="Method numdifftools.core._PartialDerivative._partial_der()=numdifftools.core._PartialDerivative-class.html#_partial_der"><a title="numdifftools.core._PartialDerivative._partial_der" class="py-name" href="#" onclick="return doclink('link-47', '_partial_der', 'link-47');">_partial_der</a></tt><tt class="py-op">(</tt><tt class="py-name">x00</tt><tt class="py-op">)</tt> </tt>
</div></div><a name="L1066"></a><tt class="py-lineno">1066</tt>  <tt class="py-line"> </tt>
<a name="L1067"></a><tt class="py-lineno">1067</tt>  <tt class="py-line"> </tt>
<a name="Hessdiag"></a><div id="Hessdiag-def"><a name="L1068"></a><tt class="py-lineno">1068</tt> <a class="py-toggle" href="#" id="Hessdiag-toggle" onclick="return toggle('Hessdiag');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="numdifftools.core.Hessdiag-class.html">Hessdiag</a><tt class="py-op">(</tt><tt class="py-base-class">_PartialDerivative</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Hessdiag-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="Hessdiag-expanded"><a name="L1069"></a><tt class="py-lineno">1069</tt>  <tt class="py-line">    <tt id="link-48" class="py-name" targets="Variable numdifftools.core.Hessdiag._hessdiag_txt=numdifftools.core.Hessdiag-class.html#_hessdiag_txt"><a title="numdifftools.core.Hessdiag._hessdiag_txt" class="py-name" href="#" onclick="return doclink('link-48', '_hessdiag_txt', 'link-48');">_hessdiag_txt</a></tt> <tt class="py-op">=</tt> <tt id="link-49" class="py-name"><a title="numdifftools.core._Derivative" class="py-name" href="#" onclick="return doclink('link-49', '_Derivative', 'link-27');">_Derivative</a></tt><tt class="py-op">.</tt><tt id="link-50" class="py-name"><a title="numdifftools.core.Derivative.__doc__
numdifftools.core.Gradient.__doc__
numdifftools.core.Hessdiag.__doc__
numdifftools.core.Hessian.__doc__
numdifftools.core.Jacobian.__doc__" class="py-name" href="#" onclick="return doclink('link-50', '__doc__', 'link-26');">__doc__</a></tt><tt class="py-op">.</tt><tt class="py-name">partition</tt><tt class="py-op">(</tt><tt class="py-string">'\n'</tt><tt class="py-op">)</tt><tt class="py-op">[</tt><tt class="py-number">2</tt><tt class="py-op">]</tt><tt class="py-op">.</tt><tt class="py-name">replace</tt><tt class="py-op">(</tt> </tt>
<a name="L1070"></a><tt class="py-lineno">1070</tt>  <tt class="py-line">        <tt class="py-string">'Integer from 1 to 4 defining derivative order. (Default 1)'</tt><tt class="py-op">,</tt> </tt>
<a name="L1071"></a><tt class="py-lineno">1071</tt>  <tt class="py-line">        <tt class="py-string">'Derivative order is always 2'</tt><tt class="py-op">)</tt> </tt>
<a name="L1072"></a><tt class="py-lineno">1072</tt>  <tt class="py-line">    <tt id="link-51" class="py-name"><a title="numdifftools.core.Derivative.__doc__
numdifftools.core.Gradient.__doc__
numdifftools.core.Hessdiag.__doc__
numdifftools.core.Hessian.__doc__
numdifftools.core.Jacobian.__doc__" class="py-name" href="#" onclick="return doclink('link-51', '__doc__', 'link-26');">__doc__</a></tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt> <tt class="py-comment">#@ReservedAssignment</tt> </tt>
<a name="L1073"></a><tt class="py-lineno">1073</tt>  <tt class="py-line">    <tt class="py-string">'''Estimate diagonal elements of Hessian of fun at x0,</tt> </tt>
<a name="L1074"></a><tt class="py-lineno">1074</tt>  <tt class="py-line"><tt class="py-string">    with error estimate</tt> </tt>
<a name="L1075"></a><tt class="py-lineno">1075</tt>  <tt class="py-line"><tt class="py-string">    '''</tt> <tt class="py-op">+</tt> <tt id="link-52" class="py-name"><a title="numdifftools.core.Hessdiag._hessdiag_txt" class="py-name" href="#" onclick="return doclink('link-52', '_hessdiag_txt', 'link-48');">_hessdiag_txt</a></tt> <tt class="py-op">+</tt> <tt class="py-string">'''</tt> </tt>
<a name="L1076"></a><tt class="py-lineno">1076</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1077"></a><tt class="py-lineno">1077</tt>  <tt class="py-line"><tt class="py-string">    HESSDIAG return a vector of second order partial derivatives of fun.</tt> </tt>
<a name="L1078"></a><tt class="py-lineno">1078</tt>  <tt class="py-line"><tt class="py-string">    These are the diagonal elements of the Hessian matrix, evaluated</tt> </tt>
<a name="L1079"></a><tt class="py-lineno">1079</tt>  <tt class="py-line"><tt class="py-string">    at x0.  When all that you want are the diagonal elements of the hessian</tt> </tt>
<a name="L1080"></a><tt class="py-lineno">1080</tt>  <tt class="py-line"><tt class="py-string">    matrix, it will be more efficient to call HESSDIAG than HESSIAN.</tt> </tt>
<a name="L1081"></a><tt class="py-lineno">1081</tt>  <tt class="py-line"><tt class="py-string">    HESSDIAG uses DERIVATIVE to provide both second derivative estimates</tt> </tt>
<a name="L1082"></a><tt class="py-lineno">1082</tt>  <tt class="py-line"><tt class="py-string">    and error estimates.</tt> </tt>
<a name="L1083"></a><tt class="py-lineno">1083</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1084"></a><tt class="py-lineno">1084</tt>  <tt class="py-line"><tt class="py-string">    Assumptions</tt> </tt>
<a name="L1085"></a><tt class="py-lineno">1085</tt>  <tt class="py-line"><tt class="py-string">    ------------</tt> </tt>
<a name="L1086"></a><tt class="py-lineno">1086</tt>  <tt class="py-line"><tt class="py-string">    fun : SCALAR analytical function to differentiate.</tt> </tt>
<a name="L1087"></a><tt class="py-lineno">1087</tt>  <tt class="py-line"><tt class="py-string">        fun must be a function of the vector or array x0,</tt> </tt>
<a name="L1088"></a><tt class="py-lineno">1088</tt>  <tt class="py-line"><tt class="py-string">        but it needs not to be vectorized.</tt> </tt>
<a name="L1089"></a><tt class="py-lineno">1089</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1090"></a><tt class="py-lineno">1090</tt>  <tt class="py-line"><tt class="py-string">    x0 : vector location at which to differentiate fun</tt> </tt>
<a name="L1091"></a><tt class="py-lineno">1091</tt>  <tt class="py-line"><tt class="py-string">        If x0 is an N x M array, then fun is assumed to be</tt> </tt>
<a name="L1092"></a><tt class="py-lineno">1092</tt>  <tt class="py-line"><tt class="py-string">        a function of N*M variables.</tt> </tt>
<a name="L1093"></a><tt class="py-lineno">1093</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1094"></a><tt class="py-lineno">1094</tt>  <tt class="py-line"><tt class="py-string">    Examples</tt> </tt>
<a name="L1095"></a><tt class="py-lineno">1095</tt>  <tt class="py-line"><tt class="py-string">    --------</tt> </tt>
<a name="L1096"></a><tt class="py-lineno">1096</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; import numpy as np</tt> </tt>
<a name="L1097"></a><tt class="py-lineno">1097</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; import numdifftools as nd</tt> </tt>
<a name="L1098"></a><tt class="py-lineno">1098</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; fun = lambda x : x[0] + x[1]**2 + x[2]**3</tt> </tt>
<a name="L1099"></a><tt class="py-lineno">1099</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; ddfun = lambda x : np.asarray((0, 2, 6*x[2]))</tt> </tt>
<a name="L1100"></a><tt class="py-lineno">1100</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; Hfun = nd.Hessdiag(fun)</tt> </tt>
<a name="L1101"></a><tt class="py-lineno">1101</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; hd = Hfun([1,2,3]) # HD = [ 0,2,18]</tt> </tt>
<a name="L1102"></a><tt class="py-lineno">1102</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; hd</tt> </tt>
<a name="L1103"></a><tt class="py-lineno">1103</tt>  <tt class="py-line"><tt class="py-string">    array([  0.,   2.,  18.])</tt> </tt>
<a name="L1104"></a><tt class="py-lineno">1104</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; np.abs(ddfun([1,2,3])-hd) &lt;= Hfun.error_estimate</tt> </tt>
<a name="L1105"></a><tt class="py-lineno">1105</tt>  <tt class="py-line"><tt class="py-string">    array([ True,  True,  True], dtype=bool)</tt> </tt>
<a name="L1106"></a><tt class="py-lineno">1106</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1107"></a><tt class="py-lineno">1107</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1108"></a><tt class="py-lineno">1108</tt>  <tt class="py-line"><tt class="py-string">    See also</tt> </tt>
<a name="L1109"></a><tt class="py-lineno">1109</tt>  <tt class="py-line"><tt class="py-string">    --------</tt> </tt>
<a name="L1110"></a><tt class="py-lineno">1110</tt>  <tt class="py-line"><tt class="py-string">    Gradient, Derivative, Hessian, Jacobian</tt> </tt>
<a name="L1111"></a><tt class="py-lineno">1111</tt>  <tt class="py-line"><tt class="py-string">    '''</tt><tt class="py-op">)</tt> </tt>
<a name="L1112"></a><tt class="py-lineno">1112</tt>  <tt class="py-line"><tt class="py-comment">##    def __init__(self,fun,**kwds):</tt> </tt>
<a name="L1113"></a><tt class="py-lineno">1113</tt>  <tt class="py-line"><tt class="py-comment">##        super(Hessdiag,self).__init__(fun,**kwds)</tt> </tt>
<a name="L1114"></a><tt class="py-lineno">1114</tt>  <tt class="py-line"><tt class="py-comment">##        self.vectorized = False</tt> </tt>
<a name="L1115"></a><tt class="py-lineno">1115</tt>  <tt class="py-line"><tt class="py-comment">##        self.n = 2</tt> </tt>
<a name="L1116"></a><tt class="py-lineno">1116</tt>  <tt class="py-line"> </tt>
<a name="Hessdiag.__call__"></a><div id="Hessdiag.__call__-def"><a name="L1117"></a><tt class="py-lineno">1117</tt> <a class="py-toggle" href="#" id="Hessdiag.__call__-toggle" onclick="return toggle('Hessdiag.__call__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core.Hessdiag-class.html#__call__">__call__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x00</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Hessdiag.__call__-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="Hessdiag.__call__-expanded"><a name="L1118"></a><tt class="py-lineno">1118</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-53" class="py-name" targets="Method numdifftools.core.Hessdiag.hessdiag()=numdifftools.core.Hessdiag-class.html#hessdiag"><a title="numdifftools.core.Hessdiag.hessdiag" class="py-name" href="#" onclick="return doclink('link-53', 'hessdiag', 'link-53');">hessdiag</a></tt><tt class="py-op">(</tt><tt class="py-name">x00</tt><tt class="py-op">)</tt> </tt>
</div><a name="L1119"></a><tt class="py-lineno">1119</tt>  <tt class="py-line">         </tt>
<a name="Hessdiag.hessdiag"></a><div id="Hessdiag.hessdiag-def"><a name="L1120"></a><tt class="py-lineno">1120</tt> <a class="py-toggle" href="#" id="Hessdiag.hessdiag-toggle" onclick="return toggle('Hessdiag.hessdiag');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core.Hessdiag-class.html#hessdiag">hessdiag</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x00</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Hessdiag.hessdiag-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="Hessdiag.hessdiag-expanded"><a name="L1121"></a><tt class="py-lineno">1121</tt>  <tt class="py-line">        <tt class="py-docstring">''' Diagonal elements of Hessian matrix</tt> </tt>
<a name="L1122"></a><tt class="py-lineno">1122</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L1123"></a><tt class="py-lineno">1123</tt>  <tt class="py-line"><tt class="py-docstring">         See also derivative, gradient, hessian, jacobian</tt> </tt>
<a name="L1124"></a><tt class="py-lineno">1124</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L1125"></a><tt class="py-lineno">1125</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">n</tt> <tt class="py-op">=</tt> <tt class="py-number">2</tt> </tt>
<a name="L1126"></a><tt class="py-lineno">1126</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">vectorized</tt> <tt class="py-op">=</tt> <tt class="py-name">False</tt> </tt>
<a name="L1127"></a><tt class="py-lineno">1127</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-54" class="py-name"><a title="numdifftools.core._Derivative._initialize" class="py-name" href="#" onclick="return doclink('link-54', '_initialize', 'link-30');">_initialize</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L1128"></a><tt class="py-lineno">1128</tt>  <tt class="py-line"> </tt>
<a name="L1129"></a><tt class="py-lineno">1129</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-55" class="py-name"><a title="numdifftools.core._PartialDerivative._partial_der" class="py-name" href="#" onclick="return doclink('link-55', '_partial_der', 'link-47');">_partial_der</a></tt><tt class="py-op">(</tt><tt class="py-name">x00</tt><tt class="py-op">)</tt> </tt>
</div></div><a name="L1130"></a><tt class="py-lineno">1130</tt>  <tt class="py-line"> </tt>
<a name="L1131"></a><tt class="py-lineno">1131</tt>  <tt class="py-line">         </tt>
<a name="Hessian"></a><div id="Hessian-def"><a name="L1132"></a><tt class="py-lineno">1132</tt> <a class="py-toggle" href="#" id="Hessian-toggle" onclick="return toggle('Hessian');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="numdifftools.core.Hessian-class.html">Hessian</a><tt class="py-op">(</tt><tt class="py-base-class">Hessdiag</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Hessian-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="Hessian-expanded"><a name="L1133"></a><tt class="py-lineno">1133</tt>  <tt class="py-line">    <tt id="link-56" class="py-name" targets="Variable numdifftools.core.Hessian._hessian_txt=numdifftools.core.Hessian-class.html#_hessian_txt"><a title="numdifftools.core.Hessian._hessian_txt" class="py-name" href="#" onclick="return doclink('link-56', '_hessian_txt', 'link-56');">_hessian_txt</a></tt> <tt class="py-op">=</tt> <tt id="link-57" class="py-name"><a title="numdifftools.core._Derivative" class="py-name" href="#" onclick="return doclink('link-57', '_Derivative', 'link-27');">_Derivative</a></tt><tt class="py-op">.</tt><tt id="link-58" class="py-name"><a title="numdifftools.core.Derivative.__doc__
numdifftools.core.Gradient.__doc__
numdifftools.core.Hessdiag.__doc__
numdifftools.core.Hessian.__doc__
numdifftools.core.Jacobian.__doc__" class="py-name" href="#" onclick="return doclink('link-58', '__doc__', 'link-26');">__doc__</a></tt><tt class="py-op">.</tt><tt class="py-name">partition</tt><tt class="py-op">(</tt><tt class="py-string">'\n'</tt><tt class="py-op">)</tt><tt class="py-op">[</tt><tt class="py-number">2</tt><tt class="py-op">]</tt><tt class="py-op">.</tt><tt class="py-name">replace</tt><tt class="py-op">(</tt> </tt>
<a name="L1134"></a><tt class="py-lineno">1134</tt>  <tt class="py-line">        <tt class="py-string">'Integer from 1 to 4 defining derivative order. (Default 1)'</tt><tt class="py-op">,</tt> </tt>
<a name="L1135"></a><tt class="py-lineno">1135</tt>  <tt class="py-line">        <tt class="py-string">'Derivative order is always 2'</tt><tt class="py-op">)</tt> </tt>
<a name="L1136"></a><tt class="py-lineno">1136</tt>  <tt class="py-line">    <tt id="link-59" class="py-name"><a title="numdifftools.core.Derivative.__doc__
numdifftools.core.Gradient.__doc__
numdifftools.core.Hessdiag.__doc__
numdifftools.core.Hessian.__doc__
numdifftools.core.Jacobian.__doc__" class="py-name" href="#" onclick="return doclink('link-59', '__doc__', 'link-26');">__doc__</a></tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt> <tt class="py-comment">#@ReservedAssignment</tt> </tt>
<a name="L1137"></a><tt class="py-lineno">1137</tt>  <tt class="py-line">    <tt class="py-string">''' Estimate Hessian matrix, with error estimate</tt> </tt>
<a name="L1138"></a><tt class="py-lineno">1138</tt>  <tt class="py-line"><tt class="py-string">    '''</tt> <tt class="py-op">+</tt> <tt id="link-60" class="py-name"><a title="numdifftools.core.Hessian._hessian_txt" class="py-name" href="#" onclick="return doclink('link-60', '_hessian_txt', 'link-56');">_hessian_txt</a></tt> <tt class="py-op">+</tt> <tt class="py-string">'''</tt> </tt>
<a name="L1139"></a><tt class="py-lineno">1139</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1140"></a><tt class="py-lineno">1140</tt>  <tt class="py-line"><tt class="py-string">    HESSIAN estimate the matrix of 2nd order partial derivatives of a real</tt> </tt>
<a name="L1141"></a><tt class="py-lineno">1141</tt>  <tt class="py-line"><tt class="py-string">    valued function FUN evaluated at X0. HESSIAN is NOT a tool for frequent</tt> </tt>
<a name="L1142"></a><tt class="py-lineno">1142</tt>  <tt class="py-line"><tt class="py-string">    use on an expensive to evaluate objective function, especially in a large</tt> </tt>
<a name="L1143"></a><tt class="py-lineno">1143</tt>  <tt class="py-line"><tt class="py-string">    number of dimensions. Its computation will use roughly  O(6*n^2) function</tt> </tt>
<a name="L1144"></a><tt class="py-lineno">1144</tt>  <tt class="py-line"><tt class="py-string">    evaluations for n parameters.</tt> </tt>
<a name="L1145"></a><tt class="py-lineno">1145</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1146"></a><tt class="py-lineno">1146</tt>  <tt class="py-line"><tt class="py-string">    Assumptions</tt> </tt>
<a name="L1147"></a><tt class="py-lineno">1147</tt>  <tt class="py-line"><tt class="py-string">    -----------</tt> </tt>
<a name="L1148"></a><tt class="py-lineno">1148</tt>  <tt class="py-line"><tt class="py-string">    fun : SCALAR analytical function</tt> </tt>
<a name="L1149"></a><tt class="py-lineno">1149</tt>  <tt class="py-line"><tt class="py-string">        to differentiate. fun must be a function of the vector or array x0,</tt> </tt>
<a name="L1150"></a><tt class="py-lineno">1150</tt>  <tt class="py-line"><tt class="py-string">        but it needs not to be vectorized.</tt> </tt>
<a name="L1151"></a><tt class="py-lineno">1151</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1152"></a><tt class="py-lineno">1152</tt>  <tt class="py-line"><tt class="py-string">    x0 : vector location</tt> </tt>
<a name="L1153"></a><tt class="py-lineno">1153</tt>  <tt class="py-line"><tt class="py-string">        at which to differentiate fun</tt> </tt>
<a name="L1154"></a><tt class="py-lineno">1154</tt>  <tt class="py-line"><tt class="py-string">        If x0 is an N x M array, then fun is assumed to be a function</tt> </tt>
<a name="L1155"></a><tt class="py-lineno">1155</tt>  <tt class="py-line"><tt class="py-string">        of N*M variables.</tt> </tt>
<a name="L1156"></a><tt class="py-lineno">1156</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1157"></a><tt class="py-lineno">1157</tt>  <tt class="py-line"><tt class="py-string">    Examples</tt> </tt>
<a name="L1158"></a><tt class="py-lineno">1158</tt>  <tt class="py-line"><tt class="py-string">    --------</tt> </tt>
<a name="L1159"></a><tt class="py-lineno">1159</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; import numpy as np</tt> </tt>
<a name="L1160"></a><tt class="py-lineno">1160</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; import numdifftools as nd</tt> </tt>
<a name="L1161"></a><tt class="py-lineno">1161</tt>  <tt class="py-line"><tt class="py-string">    </tt> </tt>
<a name="L1162"></a><tt class="py-lineno">1162</tt>  <tt class="py-line"><tt class="py-string">    # Rosenbrock function, minimized at [1,1]</tt> </tt>
<a name="L1163"></a><tt class="py-lineno">1163</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; rosen = lambda x : (1.-x[0])**2 + 105*(x[1]-x[0]**2)**2</tt> </tt>
<a name="L1164"></a><tt class="py-lineno">1164</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; Hfun = nd.Hessian(rosen)</tt> </tt>
<a name="L1165"></a><tt class="py-lineno">1165</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; h = Hfun([1, 1]) </tt> </tt>
<a name="L1166"></a><tt class="py-lineno">1166</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; h</tt> </tt>
<a name="L1167"></a><tt class="py-lineno">1167</tt>  <tt class="py-line"><tt class="py-string">    array([[ 842., -420.],</tt> </tt>
<a name="L1168"></a><tt class="py-lineno">1168</tt>  <tt class="py-line"><tt class="py-string">           [-420.,  210.]])</tt> </tt>
<a name="L1169"></a><tt class="py-lineno">1169</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; Hfun.error_estimate &lt; 1.e-11</tt> </tt>
<a name="L1170"></a><tt class="py-lineno">1170</tt>  <tt class="py-line"><tt class="py-string">    array([[ True,  True],</tt> </tt>
<a name="L1171"></a><tt class="py-lineno">1171</tt>  <tt class="py-line"><tt class="py-string">           [ True,  True]], dtype=bool)</tt> </tt>
<a name="L1172"></a><tt class="py-lineno">1172</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1173"></a><tt class="py-lineno">1173</tt>  <tt class="py-line"><tt class="py-string">    # cos(x-y), at (0,0)</tt> </tt>
<a name="L1174"></a><tt class="py-lineno">1174</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; cos = np.cos</tt> </tt>
<a name="L1175"></a><tt class="py-lineno">1175</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; fun = lambda xy : cos(xy[0]-xy[1])</tt> </tt>
<a name="L1176"></a><tt class="py-lineno">1176</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; Hfun2 = nd.Hessian(fun)</tt> </tt>
<a name="L1177"></a><tt class="py-lineno">1177</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; h2 = Hfun2([0, 0]) </tt> </tt>
<a name="L1178"></a><tt class="py-lineno">1178</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; h2</tt> </tt>
<a name="L1179"></a><tt class="py-lineno">1179</tt>  <tt class="py-line"><tt class="py-string">    array([[-1.,  1.],</tt> </tt>
<a name="L1180"></a><tt class="py-lineno">1180</tt>  <tt class="py-line"><tt class="py-string">           [ 1., -1.]])</tt> </tt>
<a name="L1181"></a><tt class="py-lineno">1181</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; np.abs(h2-np.array([[-1,  1],[ 1, -1]])) &lt; Hfun2.error_estimate</tt> </tt>
<a name="L1182"></a><tt class="py-lineno">1182</tt>  <tt class="py-line"><tt class="py-string">    array([[ True,  True],</tt> </tt>
<a name="L1183"></a><tt class="py-lineno">1183</tt>  <tt class="py-line"><tt class="py-string">           [ True,  True]], dtype=bool)</tt> </tt>
<a name="L1184"></a><tt class="py-lineno">1184</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1185"></a><tt class="py-lineno">1185</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; Hfun2.romberg_terms = 3</tt> </tt>
<a name="L1186"></a><tt class="py-lineno">1186</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; h3 = Hfun2([0,0])</tt> </tt>
<a name="L1187"></a><tt class="py-lineno">1187</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; h3</tt> </tt>
<a name="L1188"></a><tt class="py-lineno">1188</tt>  <tt class="py-line"><tt class="py-string">    array([[-1.,  1.],</tt> </tt>
<a name="L1189"></a><tt class="py-lineno">1189</tt>  <tt class="py-line"><tt class="py-string">           [ 1., -1.]])</tt> </tt>
<a name="L1190"></a><tt class="py-lineno">1190</tt>  <tt class="py-line"><tt class="py-string">    &gt;&gt;&gt; np.abs(h3-np.array([[-1,  1],[ 1, -1]])) &lt; Hfun2.error_estimate</tt> </tt>
<a name="L1191"></a><tt class="py-lineno">1191</tt>  <tt class="py-line"><tt class="py-string">    array([[ True,  True],</tt> </tt>
<a name="L1192"></a><tt class="py-lineno">1192</tt>  <tt class="py-line"><tt class="py-string">           [ True,  True]], dtype=bool)</tt> </tt>
<a name="L1193"></a><tt class="py-lineno">1193</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1194"></a><tt class="py-lineno">1194</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1195"></a><tt class="py-lineno">1195</tt>  <tt class="py-line"><tt class="py-string">    See also</tt> </tt>
<a name="L1196"></a><tt class="py-lineno">1196</tt>  <tt class="py-line"><tt class="py-string">    --------</tt> </tt>
<a name="L1197"></a><tt class="py-lineno">1197</tt>  <tt class="py-line"><tt class="py-string">    Gradient,</tt> </tt>
<a name="L1198"></a><tt class="py-lineno">1198</tt>  <tt class="py-line"><tt class="py-string">    Derivative,</tt> </tt>
<a name="L1199"></a><tt class="py-lineno">1199</tt>  <tt class="py-line"><tt class="py-string">    Hessdiag,</tt> </tt>
<a name="L1200"></a><tt class="py-lineno">1200</tt>  <tt class="py-line"><tt class="py-string">    Jacobian</tt> </tt>
<a name="L1201"></a><tt class="py-lineno">1201</tt>  <tt class="py-line"><tt class="py-string">    '''</tt><tt class="py-op">)</tt> </tt>
<a name="Hessian.__call__"></a><div id="Hessian.__call__-def"><a name="L1202"></a><tt class="py-lineno">1202</tt> <a class="py-toggle" href="#" id="Hessian.__call__-toggle" onclick="return toggle('Hessian.__call__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core.Hessian-class.html#__call__">__call__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x00</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Hessian.__call__-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="Hessian.__call__-expanded"><a name="L1203"></a><tt class="py-lineno">1203</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-61" class="py-name" targets="Method numdifftools.core.Hessian.hessian()=numdifftools.core.Hessian-class.html#hessian,Method numdifftools.nd_algopy.Hessian.hessian()=numdifftools.nd_algopy.Hessian-class.html#hessian,Method numdifftools.nd_scientific.Hessian.hessian()=numdifftools.nd_scientific.Hessian-class.html#hessian"><a title="numdifftools.core.Hessian.hessian
numdifftools.nd_algopy.Hessian.hessian
numdifftools.nd_scientific.Hessian.hessian" class="py-name" href="#" onclick="return doclink('link-61', 'hessian', 'link-61');">hessian</a></tt><tt class="py-op">(</tt><tt class="py-name">x00</tt><tt class="py-op">)</tt> </tt>
</div><a name="L1204"></a><tt class="py-lineno">1204</tt>  <tt class="py-line">         </tt>
<a name="Hessian.hessian"></a><div id="Hessian.hessian-def"><a name="L1205"></a><tt class="py-lineno">1205</tt> <a class="py-toggle" href="#" id="Hessian.hessian-toggle" onclick="return toggle('Hessian.hessian');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core.Hessian-class.html#hessian">hessian</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x00</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Hessian.hessian-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="Hessian.hessian-expanded"><a name="L1206"></a><tt class="py-lineno">1206</tt>  <tt class="py-line">        <tt class="py-docstring">'''Hessian matrix i.e., array of 2nd order partial derivatives</tt> </tt>
<a name="L1207"></a><tt class="py-lineno">1207</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L1208"></a><tt class="py-lineno">1208</tt>  <tt class="py-line"><tt class="py-docstring">         See also derivative, gradient, hessdiag, jacobian</tt> </tt>
<a name="L1209"></a><tt class="py-lineno">1209</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L1210"></a><tt class="py-lineno">1210</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L1211"></a><tt class="py-lineno">1211</tt>  <tt class="py-line"> </tt>
<a name="L1212"></a><tt class="py-lineno">1212</tt>  <tt class="py-line">        <tt class="py-name">zeros</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt> </tt>
<a name="L1213"></a><tt class="py-lineno">1213</tt>  <tt class="py-line">        <tt class="py-name">x0</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">atleast_1d</tt><tt class="py-op">(</tt><tt class="py-name">x00</tt><tt class="py-op">)</tt> </tt>
<a name="L1214"></a><tt class="py-lineno">1214</tt>  <tt class="py-line">        <tt class="py-name">nx</tt> <tt class="py-op">=</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">)</tt> </tt>
<a name="L1215"></a><tt class="py-lineno">1215</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">method</tt> <tt class="py-op">=</tt> <tt class="py-string">'central'</tt> </tt>
<a name="L1216"></a><tt class="py-lineno">1216</tt>  <tt class="py-line">        <tt class="py-comment">#sx = nx #size(x0)</tt> </tt>
<a name="L1217"></a><tt class="py-lineno">1217</tt>  <tt class="py-line"> </tt>
<a name="L1218"></a><tt class="py-lineno">1218</tt>  <tt class="py-line">        <tt class="py-comment"># get the diagonal elements of the hessian (2nd partial</tt> </tt>
<a name="L1219"></a><tt class="py-lineno">1219</tt>  <tt class="py-line">        <tt class="py-comment"># derivatives wrt each variable.)</tt> </tt>
<a name="L1220"></a><tt class="py-lineno">1220</tt>  <tt class="py-line">        <tt class="py-name">hess</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-62" class="py-name"><a title="numdifftools.core.Hessdiag.hessdiag" class="py-name" href="#" onclick="return doclink('link-62', 'hessdiag', 'link-53');">hessdiag</a></tt><tt class="py-op">(</tt><tt class="py-name">x00</tt><tt class="py-op">)</tt> </tt>
<a name="L1221"></a><tt class="py-lineno">1221</tt>  <tt class="py-line">        <tt class="py-name">err</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">error_estimate</tt> </tt>
<a name="L1222"></a><tt class="py-lineno">1222</tt>  <tt class="py-line"> </tt>
<a name="L1223"></a><tt class="py-lineno">1223</tt>  <tt class="py-line">        <tt class="py-comment"># form the eventual hessian matrix, stuffing only</tt> </tt>
<a name="L1224"></a><tt class="py-lineno">1224</tt>  <tt class="py-line">        <tt class="py-comment"># the diagonals for now.</tt> </tt>
<a name="L1225"></a><tt class="py-lineno">1225</tt>  <tt class="py-line">        <tt class="py-name">hess</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">diag</tt><tt class="py-op">(</tt><tt class="py-name">hess</tt><tt class="py-op">)</tt> </tt>
<a name="L1226"></a><tt class="py-lineno">1226</tt>  <tt class="py-line">        <tt class="py-name">err</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">diag</tt><tt class="py-op">(</tt><tt class="py-name">err</tt><tt class="py-op">)</tt> </tt>
<a name="L1227"></a><tt class="py-lineno">1227</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">nx</tt> <tt class="py-op">&lt;</tt> <tt class="py-number">2</tt> <tt class="py-op">:</tt> </tt>
<a name="L1228"></a><tt class="py-lineno">1228</tt>  <tt class="py-line">            <tt class="py-comment"># the hessian matrix is 1x1. all done</tt> </tt>
<a name="L1229"></a><tt class="py-lineno">1229</tt>  <tt class="py-line">            <tt class="py-keyword">return</tt> <tt class="py-name">hess</tt> </tt>
<a name="L1230"></a><tt class="py-lineno">1230</tt>  <tt class="py-line"> </tt>
<a name="L1231"></a><tt class="py-lineno">1231</tt>  <tt class="py-line">        <tt class="py-comment"># get the gradient vector. This is done only to decide</tt> </tt>
<a name="L1232"></a><tt class="py-lineno">1232</tt>  <tt class="py-line">        <tt class="py-comment"># on intelligent step sizes for the mixed partials</tt> </tt>
<a name="L1233"></a><tt class="py-lineno">1233</tt>  <tt class="py-line">        <tt class="py-comment">#grad = self._gradient(x00)</tt> </tt>
<a name="L1234"></a><tt class="py-lineno">1234</tt>  <tt class="py-line">        <tt class="py-name">stepsize</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">finaldelta</tt> <tt class="py-comment">#np.maximum(, 1e-4)</tt> </tt>
<a name="L1235"></a><tt class="py-lineno">1235</tt>  <tt class="py-line"> </tt>
<a name="L1236"></a><tt class="py-lineno">1236</tt>  <tt class="py-line"> </tt>
<a name="L1237"></a><tt class="py-lineno">1237</tt>  <tt class="py-line">        <tt class="py-comment">#self.romberg_terms = 4</tt> </tt>
<a name="L1238"></a><tt class="py-lineno">1238</tt>  <tt class="py-line">        <tt class="py-comment"># Get params.RombergTerms+1 estimates of the upper</tt> </tt>
<a name="L1239"></a><tt class="py-lineno">1239</tt>  <tt class="py-line">        <tt class="py-comment"># triangle of the hessian matrix</tt> </tt>
<a name="L1240"></a><tt class="py-lineno">1240</tt>  <tt class="py-line"> </tt>
<a name="L1241"></a><tt class="py-lineno">1241</tt>  <tt class="py-line">        <tt class="py-name">ndel</tt> <tt class="py-op">=</tt> <tt class="py-name">int</tt><tt class="py-op">(</tt><tt class="py-number">3.</tt> <tt class="py-op">+</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">ceil</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">n</tt> <tt class="py-op">/</tt> <tt class="py-number">2.</tt><tt class="py-op">)</tt> <tt class="py-op">+</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">order</tt> <tt class="py-op">+</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">romberg_terms</tt> <tt class="py-op">+</tt> <tt class="py-number">4</tt><tt class="py-op">)</tt> </tt>
<a name="L1242"></a><tt class="py-lineno">1242</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">method</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">==</tt> <tt class="py-string">'c'</tt><tt class="py-op">:</tt> </tt>
<a name="L1243"></a><tt class="py-lineno">1243</tt>  <tt class="py-line">            <tt class="py-name">ndel</tt> <tt class="py-op">=</tt> <tt class="py-name">ndel</tt> <tt class="py-op">-</tt> <tt class="py-number">2</tt> </tt>
<a name="L1244"></a><tt class="py-lineno">1244</tt>  <tt class="py-line">        <tt class="py-comment">#ndelMin = len(self.rombexpon) + 2</tt> </tt>
<a name="L1245"></a><tt class="py-lineno">1245</tt>  <tt class="py-line">        <tt class="py-name">ndelMin</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">romberg_terms</tt> <tt class="py-op">+</tt> <tt class="py-number">2</tt> </tt>
<a name="L1246"></a><tt class="py-lineno">1246</tt>  <tt class="py-line">        <tt class="py-name">ndel</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">maximum</tt><tt class="py-op">(</tt><tt class="py-name">ndelMin</tt><tt class="py-op">,</tt> <tt class="py-name">ndel</tt><tt class="py-op">)</tt> </tt>
<a name="L1247"></a><tt class="py-lineno">1247</tt>  <tt class="py-line">        <tt class="py-comment">#ndel = ndelMin</tt> </tt>
<a name="L1248"></a><tt class="py-lineno">1248</tt>  <tt class="py-line">        <tt class="py-name">dfac</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-number">1.0</tt> <tt class="py-op">*</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">step_ratio</tt><tt class="py-op">)</tt> <tt class="py-op">**</tt> <tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">arange</tt><tt class="py-op">(</tt><tt class="py-name">ndel</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L1249"></a><tt class="py-lineno">1249</tt>  <tt class="py-line">        <tt class="py-name">stepmax</tt> <tt class="py-op">=</tt> <tt class="py-name">stepsize</tt> <tt class="py-op">/</tt> <tt class="py-name">dfac</tt><tt class="py-op">[</tt><tt class="py-name">ndel</tt><tt class="py-op">//</tt><tt class="py-number">2</tt><tt class="py-op">]</tt> </tt>
<a name="L1250"></a><tt class="py-lineno">1250</tt>  <tt class="py-line">        <tt class="py-name">fun</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">fun</tt> </tt>
<a name="L1251"></a><tt class="py-lineno">1251</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-name">i</tt> <tt class="py-keyword">in</tt> <tt class="py-name">range</tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-name">nx</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L1252"></a><tt class="py-lineno">1252</tt>  <tt class="py-line">            <tt class="py-keyword">for</tt> <tt class="py-name">j</tt> <tt class="py-keyword">in</tt> <tt class="py-name">range</tt><tt class="py-op">(</tt><tt class="py-name">i</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L1253"></a><tt class="py-lineno">1253</tt>  <tt class="py-line">                <tt class="py-name">dij</tt> <tt class="py-op">=</tt> <tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-name">ndel</tt><tt class="py-op">)</tt> </tt>
<a name="L1254"></a><tt class="py-lineno">1254</tt>  <tt class="py-line">                <tt class="py-name">step</tt> <tt class="py-op">=</tt> <tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-name">nx</tt><tt class="py-op">)</tt> </tt>
<a name="L1255"></a><tt class="py-lineno">1255</tt>  <tt class="py-line">                <tt class="py-comment">#step[[i, j]] = stepsize[[i, j]]</tt> </tt>
<a name="L1256"></a><tt class="py-lineno">1256</tt>  <tt class="py-line">                <tt class="py-name">step</tt><tt class="py-op">[</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">,</tt> <tt class="py-name">j</tt><tt class="py-op">]</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">stepmax</tt><tt class="py-op">[</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">,</tt> <tt class="py-name">j</tt><tt class="py-op">]</tt><tt class="py-op">]</tt> </tt>
<a name="L1257"></a><tt class="py-lineno">1257</tt>  <tt class="py-line"> </tt>
<a name="L1258"></a><tt class="py-lineno">1258</tt>  <tt class="py-line">                <tt class="py-keyword">for</tt> <tt class="py-name">k</tt> <tt class="py-keyword">in</tt> <tt class="py-name">range</tt><tt class="py-op">(</tt><tt class="py-name">int</tt><tt class="py-op">(</tt><tt class="py-name">ndel</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L1259"></a><tt class="py-lineno">1259</tt>  <tt class="py-line">                    <tt class="py-name">x1</tt> <tt class="py-op">=</tt> <tt class="py-name">x0</tt> <tt class="py-op">+</tt> <tt class="py-name">step</tt> <tt class="py-op">*</tt> <tt class="py-name">dfac</tt><tt class="py-op">[</tt><tt class="py-name">k</tt><tt class="py-op">]</tt> </tt>
<a name="L1260"></a><tt class="py-lineno">1260</tt>  <tt class="py-line">                    <tt class="py-name">x2</tt> <tt class="py-op">=</tt> <tt class="py-name">x0</tt> <tt class="py-op">-</tt> <tt class="py-name">step</tt> <tt class="py-op">*</tt> <tt class="py-name">dfac</tt><tt class="py-op">[</tt><tt class="py-name">k</tt><tt class="py-op">]</tt> </tt>
<a name="L1261"></a><tt class="py-lineno">1261</tt>  <tt class="py-line">                    <tt class="py-name">step</tt><tt class="py-op">[</tt><tt class="py-name">j</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-op">-</tt><tt class="py-name">step</tt><tt class="py-op">[</tt><tt class="py-name">j</tt><tt class="py-op">]</tt> </tt>
<a name="L1262"></a><tt class="py-lineno">1262</tt>  <tt class="py-line">                    <tt class="py-name">x3</tt> <tt class="py-op">=</tt> <tt class="py-name">x0</tt> <tt class="py-op">+</tt> <tt class="py-name">step</tt> <tt class="py-op">*</tt> <tt class="py-name">dfac</tt><tt class="py-op">[</tt><tt class="py-name">k</tt><tt class="py-op">]</tt><tt class="py-op">;</tt> <tt class="py-name">step</tt> <tt class="py-op">=</tt> <tt class="py-op">-</tt><tt class="py-name">step</tt> </tt>
<a name="L1263"></a><tt class="py-lineno">1263</tt>  <tt class="py-line">                    <tt class="py-name">x4</tt> <tt class="py-op">=</tt> <tt class="py-name">x0</tt> <tt class="py-op">+</tt> <tt class="py-name">step</tt> <tt class="py-op">*</tt> <tt class="py-name">dfac</tt><tt class="py-op">[</tt><tt class="py-name">k</tt><tt class="py-op">]</tt> </tt>
<a name="L1264"></a><tt class="py-lineno">1264</tt>  <tt class="py-line">                    <tt class="py-name">step</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-op">-</tt><tt class="py-name">step</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt> </tt>
<a name="L1265"></a><tt class="py-lineno">1265</tt>  <tt class="py-line">                    <tt class="py-name">dij</tt><tt class="py-op">[</tt><tt class="py-name">k</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">x1</tt><tt class="py-op">)</tt> <tt class="py-op">+</tt> <tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">x2</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">x3</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">x4</tt><tt class="py-op">)</tt> </tt>
<a name="L1266"></a><tt class="py-lineno">1266</tt>  <tt class="py-line"> </tt>
<a name="L1267"></a><tt class="py-lineno">1267</tt>  <tt class="py-line">                <tt class="py-name">dij</tt> <tt class="py-op">=</tt> <tt class="py-name">dij</tt> <tt class="py-op">/</tt> <tt class="py-number">4</tt> <tt class="py-op">/</tt> <tt class="py-name">stepmax</tt><tt class="py-op">[</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">,</tt> <tt class="py-name">j</tt><tt class="py-op">]</tt><tt class="py-op">]</tt><tt class="py-op">.</tt><tt class="py-name">prod</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L1268"></a><tt class="py-lineno">1268</tt>  <tt class="py-line">                <tt class="py-name">dij</tt> <tt class="py-op">=</tt> <tt class="py-name">dij</tt> <tt class="py-op">/</tt> <tt class="py-op">(</tt><tt class="py-name">dfac</tt> <tt class="py-op">**</tt> <tt class="py-number">2</tt><tt class="py-op">)</tt> </tt>
<a name="L1269"></a><tt class="py-lineno">1269</tt>  <tt class="py-line"> </tt>
<a name="L1270"></a><tt class="py-lineno">1270</tt>  <tt class="py-line">                <tt class="py-comment"># Romberg extrapolation step</tt> </tt>
<a name="L1271"></a><tt class="py-lineno">1271</tt>  <tt class="py-line">                <tt class="py-name">hess_romb</tt><tt class="py-op">,</tt> <tt class="py-name">errors</tt><tt class="py-op">,</tt> <tt class="py-name">_dfac1</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-63" class="py-name"><a title="numdifftools.core._Derivative._romb_extrap" class="py-name" href="#" onclick="return doclink('link-63', '_romb_extrap', 'link-9');">_romb_extrap</a></tt><tt class="py-op">(</tt><tt class="py-name">dij</tt><tt class="py-op">,</tt> <tt class="py-name">dfac</tt><tt class="py-op">)</tt>  </tt>
<a name="L1272"></a><tt class="py-lineno">1272</tt>  <tt class="py-line">                <tt class="py-name">ind</tt> <tt class="py-op">=</tt> <tt class="py-name">errors</tt><tt class="py-op">.</tt><tt class="py-name">argmin</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L1273"></a><tt class="py-lineno">1273</tt>  <tt class="py-line"> </tt>
<a name="L1274"></a><tt class="py-lineno">1274</tt>  <tt class="py-line">                <tt class="py-name">hess</tt><tt class="py-op">[</tt><tt class="py-name">j</tt><tt class="py-op">,</tt> <tt class="py-name">i</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">hess</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">,</tt> <tt class="py-name">j</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">hess_romb</tt><tt class="py-op">[</tt><tt class="py-name">ind</tt><tt class="py-op">]</tt> </tt>
<a name="L1275"></a><tt class="py-lineno">1275</tt>  <tt class="py-line">                <tt class="py-name">err</tt><tt class="py-op">[</tt><tt class="py-name">j</tt><tt class="py-op">,</tt> <tt class="py-name">i</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">err</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">,</tt> <tt class="py-name">j</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">errors</tt><tt class="py-op">[</tt><tt class="py-name">ind</tt><tt class="py-op">]</tt> </tt>
<a name="L1276"></a><tt class="py-lineno">1276</tt>  <tt class="py-line"> </tt>
<a name="L1277"></a><tt class="py-lineno">1277</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">error_estimate</tt> <tt class="py-op">=</tt> <tt class="py-name">err</tt> </tt>
<a name="L1278"></a><tt class="py-lineno">1278</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">hess</tt> </tt>
</div></div><a name="L1279"></a><tt class="py-lineno">1279</tt>  <tt class="py-line"> </tt>
<a name="L1280"></a><tt class="py-lineno">1280</tt>  <tt class="py-line"> </tt>
<a name="L1281"></a><tt class="py-lineno">1281</tt>  <tt class="py-line"> </tt>
<a name="test_docstrings"></a><div id="test_docstrings-def"><a name="L1282"></a><tt class="py-lineno">1282</tt> <a class="py-toggle" href="#" id="test_docstrings-toggle" onclick="return toggle('test_docstrings');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.core-module.html#test_docstrings">test_docstrings</a><tt class="py-op">(</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="test_docstrings-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="test_docstrings-expanded"><a name="L1283"></a><tt class="py-lineno">1283</tt>  <tt class="py-line">    <tt class="py-keyword">import</tt> <tt class="py-name">doctest</tt> </tt>
<a name="L1284"></a><tt class="py-lineno">1284</tt>  <tt class="py-line">    <tt class="py-name">doctest</tt><tt class="py-op">.</tt><tt class="py-name">testmod</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
</div><a name="L1285"></a><tt class="py-lineno">1285</tt>  <tt class="py-line">     </tt>
<a name="L1286"></a><tt class="py-lineno">1286</tt>  <tt class="py-line"> </tt>
<a name="L1287"></a><tt class="py-lineno">1287</tt>  <tt class="py-line"><tt class="py-keyword">if</tt> <tt class="py-name">__name__</tt> <tt class="py-op">==</tt> <tt class="py-string">'__main__'</tt><tt class="py-op">:</tt> </tt>
<a name="L1288"></a><tt class="py-lineno">1288</tt>  <tt class="py-line">    <tt id="link-64" class="py-name" targets="Function numdifftools.core.test_docstrings()=numdifftools.core-module.html#test_docstrings"><a title="numdifftools.core.test_docstrings" class="py-name" href="#" onclick="return doclink('link-64', 'test_docstrings', 'link-64');">test_docstrings</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L1289"></a><tt class="py-lineno">1289</tt>  <tt class="py-line"> </tt><script type="text/javascript">
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